1 2 3 4 5 6 7 8 9 10

Caloric capacity (J/kgK) 403.249 404.328 405.291 405.673 406.355 406.766 405.722 406.045 406.543 406.551

6892 6613 6407 6333 6211 6142 6324 6265 6179 6178

13. Thermal conductivity analysis of sample in quenched state (Table 6)

cooling process, the stored energy to be used in DSSME goal. 14. Induction of SME—deformation with imposed elongation

Figure 19. Optical microstructure, in quenched state, HNO3 30% attack, (100).

Table 6. Thermal conductivity of sample in quenched state.

15. Checking of SME through dilatometric analysis

of arrow head (Figure 19).

model [2] (Table 7) (Figure 21).

used parts from SMA, Cu-based.

Thermal conductivity

(W/mK)

11. Diffractometric analysis of sample in quenched state

The presence of chemical compounds is distinguished with the formula:


12. Structural analysis of quenched sample through optical and SEM microscopy

Figure 17. Primary heat treatment: quenching to put into solution.

Figure 18. Chemical compounds distribution for Cu75Zn18Al6 alloy, in quenched state.

The martensitic structure from quenched sample is present, having predominantly the shape of arrow head (Figure 19).

13. Thermal conductivity analysis of sample in quenched state (Table 6)

The decrease of thermal conductivity for quenched sample more than six times over cast sample or forged sample, transform the SMA in a thermal barrier, following in the heatingcooling process, the stored energy to be used in DSSME goal.

14. Induction of SME—deformation with imposed elongation

After the heat treatment, the samples were subjected to an elongation with 3% deformation grade (Figure 20). The controlled elongation was realized on a traction machine, Instron 3382 model [2] (Table 7) (Figure 21).

15. Checking of SME through dilatometric analysis

parameters of heat treatments are the following: (1) heating with furnace until 800C; (2) maintaining for temperature uniformization and finishing the structural transformation, for

an hour; (3) rapid cooling in water at ambiance temperature (Figures 17 and 18).

12. Structural analysis of quenched sample through optical and SEM microscopy

The presence of chemical compounds is distinguished with the formula:

11. Diffractometric analysis of sample in quenched state

Figure 17. Primary heat treatment: quenching to put into solution.

Figure 18. Chemical compounds distribution for Cu75Zn18Al6 alloy, in quenched state.

• aluminum-copper AlCu3 by 42.8%

• copper-zinc Cu5Zn8 by 51.2%

34 Shape-Memory Materials

The dilatometric analysis records the length modifications for a sample, when it is exposed to a temperature variation. This modification of length can be reversible. Through dilatometric analysis can determine the transformation points in solid states, specific to the analyzed alloy. The determination of these transformation points is important for the applications in which are used parts from SMA, Cu-based.

The dilatometric analysis of Cu75Zn18Al6 alloy was made on a differential dilatometer, Linseis L75H/1400 model [3]. In the heating time, with a constant heating rate (5C/min), the alloy

Figure 19. Optical microstructure, in quenched state, HNO3 30% attack, (100).


Table 6. Thermal conductivity of sample in quenched state.

Figure 20. SEM microstructure, in quenched state, HNO3 30% attack, (1000).


7. Thermal-mechanical fatigue of Cu75Zn18Al6 alloy

The samples (Figure 7) used for thermal-mechanical fatigue tests are falling in dimensional class of samples which can be used for dilatometric analysis (10–50 mm length, 3–6 mm diameter). The experiments were made on a prototype installation (Figure 8), designed and special manufactured for these tests. After education, the samples were subjected to a variable

Figure 22. Sample dilatogram, after quenching to put in solution and controlled deformation (3% grade), without fatigue

Aspects Regarding Thermal-Mechanical Fatigue of Shape Memory Alloys

http://dx.doi.org/10.5772/intechopen.77991

37

After a certain number of cycles, the samples were analyzed on dilatometer, studying the contraction modifications on the heating time and the variation of temperatures domain for the critical points. With a hot/cold air installation (constructive element from prototype installation), the Cu75Zn18Al6 sample is heating up to 150C, and then cooled until 40C. The

The control of testing parameters (heating and cooling parameters, number of cycles, test times) was made with specific software, XMEM. The load to which it was subjected the sample is kept constant for all the thermal-mechanical fatigue tests. Also with XMEM software, was made and synchronization of mechanical load cycle with thermal cycle: when the sample is mechanical loaded, is started the heating. The sample stays under load during the heating time, up to 150C final temperature. After this moment, the sample is cooled, and the mechanical load is removed, using motor-reducing gear-arm system to lift the weights (Figure 8). While the mechanical load is canceled, the sample is cooling until 40C final

7.1. Testing conditions

cycles.

temperature.

number of thermal-mechanical fatigue cycles.

heating rate is 15C/min, and cooling rate is 30C/min.

Table 7. Mechanical characteristics.

Figure 21. Load-elongation diagram.

presents a contraction phenomenon which starts at the start temperature of martensite-austenite transformation and finishes when the alloy does not present a martensitic structure (Figure 22).

The Cu75Zn18Al6 alloy presents the martensite-austenite transformation domain between 65.8C and 102.2C. The maximum contraction, between two temperature values, is 30.7 μm.

Figure 22. Sample dilatogram, after quenching to put in solution and controlled deformation (3% grade), without fatigue cycles.

## 7. Thermal-mechanical fatigue of Cu75Zn18Al6 alloy

#### 7.1. Testing conditions

presents a contraction phenomenon which starts at the start temperature of martensite-austenite transformation and finishes when the alloy does not present a martensitic structure (Figure 22). The Cu75Zn18Al6 alloy presents the martensite-austenite transformation domain between 65.8C and 102.2C. The maximum contraction, between two temperature values, is 30.7 μm.

Maximum force Fmax (N) Young modulus E (MPa) Maximum load σ<sup>r</sup> (MPa) Elongation (%)

3576.16 20908.02 284.58 3

Figure 20. SEM microstructure, in quenched state, HNO3 30% attack, (1000).

Table 7. Mechanical characteristics.

36 Shape-Memory Materials

Figure 21. Load-elongation diagram.

The samples (Figure 7) used for thermal-mechanical fatigue tests are falling in dimensional class of samples which can be used for dilatometric analysis (10–50 mm length, 3–6 mm diameter). The experiments were made on a prototype installation (Figure 8), designed and special manufactured for these tests. After education, the samples were subjected to a variable number of thermal-mechanical fatigue cycles.

After a certain number of cycles, the samples were analyzed on dilatometer, studying the contraction modifications on the heating time and the variation of temperatures domain for the critical points. With a hot/cold air installation (constructive element from prototype installation), the Cu75Zn18Al6 sample is heating up to 150C, and then cooled until 40C. The heating rate is 15C/min, and cooling rate is 30C/min.

The control of testing parameters (heating and cooling parameters, number of cycles, test times) was made with specific software, XMEM. The load to which it was subjected the sample is kept constant for all the thermal-mechanical fatigue tests. Also with XMEM software, was made and synchronization of mechanical load cycle with thermal cycle: when the sample is mechanical loaded, is started the heating. The sample stays under load during the heating time, up to 150C final temperature. After this moment, the sample is cooled, and the mechanical load is removed, using motor-reducing gear-arm system to lift the weights (Figure 8). While the mechanical load is canceled, the sample is cooling until 40C final temperature.

#### 7.2. Experimental results

After an arbitrary number of thermal-mechanical fatigue cycles, the sample is analyzed on dilatometer to record the modifications of shape memory properties, which appear after the thermal-mechanical synchronized cycles.

The conditions for dilatometric analysis are the following: (1) the sample is heating from ambiance temperature (25–30C) up to 150C; (2) the heating rate for SMA is imposed to 5C/ min; (3) the sample cooling is made in same time with the furnace of dilatometer (the cooling rate is 10C/min); (4) after cooling the sample is subjected to other number of thermalmechanical fatigue cycles; (5) with the specific software, can obtain dilatogram with the information about the analyzed SMA (Figures 23–25).

Figure 25. Dilatogram after 12,685 thermal-mechanical fatigue cycles.

Number of load cycles N Maximum contraction values Δl (μm) Transformation temperatures (C)

 30.70 65.8 102.2 80.10 40.7 99.5 79.70 40.2 67.0 57.70 42.3 56.8 83.80 37.7 68.0 71.30 42.0 69.5 74.90 44.0 72.2 80.00 47.3 72.3 88.70 49.2 75.3 103.50 45.0 71.7 96.10 47.9 77.0 103.60 40.1 70.2 80.20 48.5 73.3 83.20 45.3 72.3 118.70 39.9 80.1 159.40 37.3 75.9 127.30 43.8 72.2 165.00 36.8 71.3 149.10 42.4 77.5 155.10 42.3 83.8 186.30 42.9 79.8 175.90 33.9 82.3

Ms Af

Aspects Regarding Thermal-Mechanical Fatigue of Shape Memory Alloys

http://dx.doi.org/10.5772/intechopen.77991

39

Figure 23. Dilatogram after 100 thermal-mechanical fatigue cycles.

Figure 24. Dilatogram after 6985 thermal-mechanical fatigue cycles.

Aspects Regarding Thermal-Mechanical Fatigue of Shape Memory Alloys http://dx.doi.org/10.5772/intechopen.77991 39

Figure 25. Dilatogram after 12,685 thermal-mechanical fatigue cycles.

7.2. Experimental results

38 Shape-Memory Materials

thermal-mechanical synchronized cycles.

information about the analyzed SMA (Figures 23–25).

Figure 23. Dilatogram after 100 thermal-mechanical fatigue cycles.

Figure 24. Dilatogram after 6985 thermal-mechanical fatigue cycles.

After an arbitrary number of thermal-mechanical fatigue cycles, the sample is analyzed on dilatometer to record the modifications of shape memory properties, which appear after the

The conditions for dilatometric analysis are the following: (1) the sample is heating from ambiance temperature (25–30C) up to 150C; (2) the heating rate for SMA is imposed to 5C/ min; (3) the sample cooling is made in same time with the furnace of dilatometer (the cooling rate is 10C/min); (4) after cooling the sample is subjected to other number of thermalmechanical fatigue cycles; (5) with the specific software, can obtain dilatogram with the



Centralizing the maximum contraction values, after various number of thermal-mechanical

Aspects Regarding Thermal-Mechanical Fatigue of Shape Memory Alloys

http://dx.doi.org/10.5772/intechopen.77991

41

After 12,685 thermal-mechanical fatigue cycles, on sample surface appeared some microcracks (Figure 27). The experimental tests were stopped. If it continued, these micro-cracks will evolve in the analyzed sample and finally will have his breaking. Figure 27 presents the

• The Cu75Zn18Al6 studied alloy was obtained through classic elaboration, on an induction furnace, using alloying elements with high purity. Any influence in elaboration process, with modifications in percents calculus of alloying elements, can lead to obtaining an alloy with SME. A variation with 1% for aluminum or zinc can modify the critical points.

• For thermal-mechanical fatigue tests of SMA, a prototype installation has been designed and realized. The fatigue tests were completed with dilatometric analysis to highlight the

• The Cu75Zn18Al6 is a ternary alloy and the structure contains inter-metallic compounds,

• After a hot plastic deformation (forging at 850–800C), the structure is finishing and contains the following compounds: AlCu3 (20.5%), Cu5Zn8 (33.3%), α-Cu0.61Zn0.39

• After quenching to put into solution, in the structure, AlCu3 (42.8%) and Cu5Zn8 (51.2%)

• Regarding the medium thermal conductivity can remark the following: (1) in cast state: 41.06 [W/mK]; (2) in forged state: 36.79 [W/mK]; (3) in quenched state: 6.35 [W/mK] (Tables 4–6). The decrease of thermal conductivity for quenched sample more than six times over cast sample or forged sample. This fact transform this SMA in a thermal barrier, following in the heating-cooling process, the stored energy can be used in DSSME goal. • The structure or Cu75Zn18Al6 alloy was analyzed through optical and SEM microscopy. The microstructures present the modifications of grains orientation and geometrical dimensions of martensite variants. The phenomenon is owed to the appearance of induced martensite under load, together with martensite thermal formed. The cast structure has a high granu-

• After hot plastic deformation through forging, the grains dimension are not modify,

Although the SMAs have a large application domain, the obtaining of parts made from SMAs at industrial level is limited due to processing difficulties. The good shape memory properties

can guarantee the functioning time for various parts, used in industrial applications.

like Cu5Zn8 and Al4Cu9, for the sample in cast state (Figure 10).

lation, with defects like goals, pores and chemical segregations.

unless their orientation on deformation direction.

fatigue cycles, can draw the fatigue curve for Cu75Zn18Al6 alloy (Table 8) (Figure 26).

aspect of micro-cracks, at different magnitudes.

8. Conclusions

deteriorations of SME.

are found (Figure 18).

(25.6%) and CuZn (20.6%) (Figure 14).

Table 8. Measured parameters in fatigue study.

Figure 26. Variation of maximum contraction according the number of load cycles.

Figure 27. Micro-cracks on sample surface, after 12,865 fatigue cycles: (a) 500 and (b) 1000.

Centralizing the maximum contraction values, after various number of thermal-mechanical fatigue cycles, can draw the fatigue curve for Cu75Zn18Al6 alloy (Table 8) (Figure 26).

After 12,685 thermal-mechanical fatigue cycles, on sample surface appeared some microcracks (Figure 27). The experimental tests were stopped. If it continued, these micro-cracks will evolve in the analyzed sample and finally will have his breaking. Figure 27 presents the aspect of micro-cracks, at different magnitudes.

## 8. Conclusions

Number of load cycles N Maximum contraction values Δl (μm) Transformation temperatures (C)

8068 150.80 37.2 76.7 9355 134.20 29.4 73.3 10,948 123.00 28.5 81.6 11,321 123.70 26.0 73.5 12,209 69.60 28.0 64.0 12,865 97.40 26.6 65.3

Table 8. Measured parameters in fatigue study.

40 Shape-Memory Materials

Figure 26. Variation of maximum contraction according the number of load cycles.

Figure 27. Micro-cracks on sample surface, after 12,865 fatigue cycles: (a) 500 and (b) 1000.

Ms Af


Although the SMAs have a large application domain, the obtaining of parts made from SMAs at industrial level is limited due to processing difficulties. The good shape memory properties can guarantee the functioning time for various parts, used in industrial applications.

## Author details

Petrică Vizureanu\*, Dragoș-Cristian Achiței, Mirabela-Georgiana Minciună and Manuela-Cristina Perju

\*Address all correspondence to: peviz2002@yahoo.com

"Gheorghe Asachi" Technical University of Iași, Romania

## References

[1] Achiței DC, Abdullah MMA, Sandu AV, Vizureanu P, Abdullah A. On the fatigue of shape memory alloys. Advanced Materials Engineering and Technology II. 2014;594-595:133. DOI: 10.4028/www.scientific.net/KEM.594-595.133

**Chapter 3**

Provisional chapter

**Modeling of the Two-Way Shape Memory Effect**

DOI: 10.5772/intechopen.75657

The shape memory alloys (SMA) are distinguished from other conventional materials by a singular behavior which takes many forms depending on the thermomechanical load. The two-way shape memory effect is one of these forms. The interest that exhibits this behavior is that the material can remember two states, so this leads to many industrial applications. This thermoelastic property is driven by the temperature under residual stress of education. To model this effect in 3D, we considered stress and temperature as control variables and the fraction of martensite as internal variable; choosing Gibbs free energy expression and applying thermodynamic principles with transformation criteria have permitted to write the constitutive equations that control this behavior. The constructed model is then numerically simulated, and finally, the proposed model appears applicable

Shape memory alloys (SMA) as they are called are a kind of particular materials which have a singular behavior, they can be largely deformed (about 10%) under an applied mechanical, a simple heating is sufficient to recover the previous form, that is why they are called that way. By varying controlled parameters (stress and temperature), these alloys can exhibit other properties like pseudoelasticity, two-way shape memory effect, one-way shape memory effect

These properties derive from phase transformations, i.e., higher temperature phase (austenite)

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Modeling of the Two-Way Shape Memory Effect

Meddour Belkacem and Brek Samir

Meddour Belkacem and Brek Samir

http://dx.doi.org/10.5772/intechopen.75657

Abstract

in engineering.

[1, 2], and reorientation effect [3].

to lower temperature phase (martensite).

1. Introduction

Additional information is available at the end of the chapter

Keywords: two-way, simulation, hysteresis, transformation

Additional information is available at the end of the chapter


#### **Modeling of the Two-Way Shape Memory Effect** Modeling of the Two-Way Shape Memory Effect

DOI: 10.5772/intechopen.75657

#### Meddour Belkacem and Brek Samir Meddour Belkacem and Brek Samir

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75657

#### Abstract

Author details

42 Shape-Memory Materials

References

Manuela-Cristina Perju

Petrică Vizureanu\*, Dragoș-Cristian Achiței, Mirabela-Georgiana Minciună and

[1] Achiței DC, Abdullah MMA, Sandu AV, Vizureanu P, Abdullah A. On the fatigue of shape memory alloys. Advanced Materials Engineering and Technology II. 2014;594-595:133.

[2] Samoilă C, Cotfas P, Cotfas D, Ursuțiu D, Vizureanu P, Aliaje cu memoria formei; 2011;

[7] Available from: https://www.zeiss.com/microscopy/us/products/light-microscopes/axio-

\*Address all correspondence to: peviz2002@yahoo.com

"Gheorghe Asachi" Technical University of Iași, Romania

DOI: 10.4028/www.scientific.net/KEM.594-595.133

[4] Available from: http://standardservice.ro/spectrometre/

[3] Available from: https://www.linseis.com/

observer-for-materials.html

Brasov, Editura Universității Transilvania. ISBN 978-973-598-934-7

[5] Available from: http://www.panalytical.com/Xray-diffractometers.htm [6] Available from: http://ctherm.com/products/tci\_thermal\_conductivity/

[8] Available from: https://www.tescan.com/en-us/technology/sem/vega3

The shape memory alloys (SMA) are distinguished from other conventional materials by a singular behavior which takes many forms depending on the thermomechanical load. The two-way shape memory effect is one of these forms. The interest that exhibits this behavior is that the material can remember two states, so this leads to many industrial applications. This thermoelastic property is driven by the temperature under residual stress of education. To model this effect in 3D, we considered stress and temperature as control variables and the fraction of martensite as internal variable; choosing Gibbs free energy expression and applying thermodynamic principles with transformation criteria have permitted to write the constitutive equations that control this behavior. The constructed model is then numerically simulated, and finally, the proposed model appears applicable in engineering.

Keywords: two-way, simulation, hysteresis, transformation

## 1. Introduction

Shape memory alloys (SMA) as they are called are a kind of particular materials which have a singular behavior, they can be largely deformed (about 10%) under an applied mechanical, a simple heating is sufficient to recover the previous form, that is why they are called that way.

By varying controlled parameters (stress and temperature), these alloys can exhibit other properties like pseudoelasticity, two-way shape memory effect, one-way shape memory effect [1, 2], and reorientation effect [3].

These properties derive from phase transformations, i.e., higher temperature phase (austenite) to lower temperature phase (martensite).

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

It is observed that these phase transformations do not occur with diffusion but rather with displacement, i.e., displacement at a distance less than interatomic [4, 5].

These important properties made them requested materials in various fields such as biomedical automotive industry, fire watch devices, aeronautics, and medical devices [6].

Two-way shape memory effect is obtained after the alloy is subjected to an education [7], i.e., to a cyclic thermal load under a constant mechanical load (Figure 1).

It should be noted that the previous education is performed to create a field of internal stresses, which will substitute the macroscopic ones; under a cyclic thermal load, the alloy will remember two states: one is at lower temperature (martensite) and the other at higher temperature (austenite) (Figure 2).

The next steps in this paper are to build the constitutive model and simulate it using an algorithm; regarding model parameters, we will use the work of [8].

## 2. Methods and materials

#### 2.1. Constitutive equations

Let us choose the following free energy expression:

$$\mathbf{G}(\sigma = \sigma\_{00}, \mathbf{T}, \mathbf{f}) = -\sigma\_{00} : \mathbf{S}\_{\mathbf{A}} : \sigma\_{00} - \mathbf{f}. \varepsilon\_{0}. \sigma\_{00} : \mathbf{R} + \mathbf{f}. \mathbf{B}. \left(\mathbf{T} - \mathbf{M}\_{s}^{0}\right) + \mathbf{C}. \mathbf{f}. (1 - \mathbf{f}) \tag{1}$$

Assuming that dissipation is associated only with transformation (fraction of martensite) [9,

Fth¼� <sup>∂</sup><sup>G</sup>

s

dt <sup>≥</sup> <sup>0</sup> (2)

<sup>s</sup> : Temperature of transformation start M- > A under stress <sup>σ</sup>. <sup>A</sup><sup>σ</sup>

Modeling of the Two-Way Shape Memory Effect http://dx.doi.org/10.5772/intechopen.75657

<sup>f</sup> : Temper-

f :

45

<sup>s</sup> : Temperature of transformation start A- > M under stress σ:M<sup>σ</sup>

<sup>∂</sup><sup>f</sup> (3)

<sup>þ</sup>Cð Þ <sup>2</sup>f�<sup>1</sup> (4)

Fdi¼Kf <sup>þ</sup><sup>H</sup> (5)

Fth¼Fdi (6)

� <sup>∂</sup><sup>G</sup> ∂f : df

Fth¼ε0:σ00:R�B: <sup>T</sup>�M<sup>0</sup>

Because of hysteresis, there is a dissipative force Fdi, which will oppose Fth.

10], the second principle of thermodynamics can be written as

Temperature of transformation finish M- > A under stress σ. ε0: Uniaxial maximum deformation.

Let us write the driving force Fth:

Figure 2. One-dimensional two-way effect. M<sup>σ</sup>

ature of transformation finish A- > M under stress σ:A<sup>σ</sup>

We choose expression of Fdi:

Transformation occurs when

We introduce the criteria functions:

Then,

SA: Fourth order tensor of complaisance; B, C: Constants to be determined, respectively, related to change of phase and interaction between austenite and martensite; f: Fraction of martensite; σ00: Tensor of stress created after education.

Figure 1. Education (50 cycles) performed on a NiTi wire under constant stress of 150 MPa [7].

Figure 2. One-dimensional two-way effect. M<sup>σ</sup> <sup>s</sup> : Temperature of transformation start A- > M under stress σ:M<sup>σ</sup> <sup>f</sup> : Temperature of transformation finish A- > M under stress σ:A<sup>σ</sup> <sup>s</sup> : Temperature of transformation start M- > A under stress <sup>σ</sup>. <sup>A</sup><sup>σ</sup> f : Temperature of transformation finish M- > A under stress σ. ε0: Uniaxial maximum deformation.

Assuming that dissipation is associated only with transformation (fraction of martensite) [9, 10], the second principle of thermodynamics can be written as

$$-\frac{\partial G}{\partial f} \cdot \frac{df}{dt} \ge 0 \tag{2}$$

Let us write the driving force Fth:

$$F^{\theta h} = -\frac{\partial G}{\partial f} \tag{3}$$

Then,

It is observed that these phase transformations do not occur with diffusion but rather with

These important properties made them requested materials in various fields such as biomed-

Two-way shape memory effect is obtained after the alloy is subjected to an education [7], i.e., to

It should be noted that the previous education is performed to create a field of internal stresses, which will substitute the macroscopic ones; under a cyclic thermal load, the alloy will remember two states: one is at lower temperature (martensite) and the other at higher temperature

The next steps in this paper are to build the constitutive model and simulate it using an

SA: Fourth order tensor of complaisance; B, C: Constants to be determined, respectively, related to change of phase and interaction between austenite and martensite; f: Fraction of martensite;

s

<sup>þ</sup> <sup>C</sup>:f:ð Þ <sup>1</sup> � <sup>f</sup> (1)

displacement, i.e., displacement at a distance less than interatomic [4, 5].

a cyclic thermal load under a constant mechanical load (Figure 1).

algorithm; regarding model parameters, we will use the work of [8].

<sup>G</sup>ð Þ¼� <sup>σ</sup> <sup>¼</sup> <sup>σ</sup>00; <sup>T</sup>; <sup>f</sup> <sup>σ</sup><sup>00</sup> : SA : <sup>σ</sup><sup>00</sup> � <sup>f</sup>:ε0:σ<sup>00</sup> : <sup>R</sup> <sup>þ</sup> <sup>f</sup>:B: <sup>T</sup> � M0

Figure 1. Education (50 cycles) performed on a NiTi wire under constant stress of 150 MPa [7].

(austenite) (Figure 2).

44 Shape-Memory Materials

2. Methods and materials

Let us choose the following free energy expression:

σ00: Tensor of stress created after education.

2.1. Constitutive equations

ical automotive industry, fire watch devices, aeronautics, and medical devices [6].

$$F^{lt} = \varepsilon\_0 \, . \sigma\_{00} \colon \mathcal{R} - B . \left( T - M\_s^0 \right) + \mathbb{C} \left( 2f - 1 \right) \tag{4}$$

Because of hysteresis, there is a dissipative force Fdi, which will oppose Fth.

We choose expression of Fdi:

$$F^{di} = \mathbf{K}f + \mathbf{H} \tag{5}$$

Transformation occurs when

$$F^{\text{thr}} = F^{\text{dir}} \tag{6}$$

We introduce the criteria functions:

$$\mathbf{q}^{\text{di}} = \mathbf{F}^{\text{th}} - \mathbf{F}^{\text{di}}; \dot{\mathbf{f}} > \mathbf{0}; \mathbf{f} \ge \mathbf{0} \; ; \; \mathbf{f} \le \mathbf{1} \tag{7}$$

At the end of the direct transformation

<sup>φ</sup>di <sup>σ</sup> <sup>¼</sup> <sup>σ</sup>0; <sup>T</sup> <sup>¼</sup> <sup>M</sup><sup>σ</sup>

At the beginning of the reverse transformation

<sup>φ</sup>in <sup>σ</sup> <sup>¼</sup> <sup>σ</sup>0; <sup>T</sup> <sup>¼</sup> <sup>A</sup><sup>σ</sup>

At the end of the reverse transformation

<sup>φ</sup>in <sup>σ</sup> <sup>¼</sup> <sup>σ</sup>0; <sup>T</sup> <sup>¼</sup> <sup>A</sup><sup>σ</sup>

2.3. Experimental data

2.4. Numerical simulation

2.4.1. One-dimensional case

M<sup>0</sup>

M<sup>0</sup>

A0

A0

B(MPa.K<sup>1</sup>

υ 0.3

Table 1. Experimental data [8, 11].

thermal load (300 ≤ T ≤ 400 K) (Figure 3).

<sup>s</sup> ð Þ <sup>K</sup> <sup>313</sup> <sup>M</sup><sup>σ</sup>

<sup>f</sup> (K) <sup>303</sup> <sup>M</sup><sup>σ</sup>

<sup>s</sup> ð Þ <sup>K</sup> <sup>315</sup> <sup>A</sup><sup>σ</sup>

<sup>f</sup> ð Þ <sup>K</sup> <sup>325</sup> <sup>A</sup><sup>σ</sup>

σ<sup>00</sup> ¼

<sup>f</sup> ; f ¼ 1 � � <sup>¼</sup> <sup>ε</sup>0:σ<sup>0</sup> : <sup>R</sup> � <sup>B</sup>: <sup>M</sup><sup>σ</sup>

σ<sup>00</sup> ¼

σ<sup>00</sup> ¼

<sup>f</sup> ; f ¼ 0 � � <sup>¼</sup> <sup>ε</sup>0:σ<sup>0</sup> : <sup>R</sup> � <sup>B</sup>: <sup>A</sup><sup>σ</sup>

is CuZnAl. The test was performed under constant stress (σ ¼ 65 MPa).

0 B@

<sup>s</sup> ; <sup>f</sup> <sup>¼</sup> <sup>1</sup> � � <sup>¼</sup> <sup>ε</sup>0:σ<sup>0</sup> : <sup>R</sup> � <sup>B</sup>: <sup>A</sup><sup>σ</sup>

0 B@

0 B@

1

1

1

Table 1 illustrates experimental data and material constants B, C, K, and H. The used material

We considered a segment of CuZnAl submitted to a constant stress (σ ¼ 65 MPa) and a

) 3.258439E-2 C(MPa) 0.18736036121 K(MPa) 4.8876464E-2

CA, T <sup>¼</sup> <sup>A</sup><sup>σ</sup>

CA, T <sup>¼</sup> <sup>A</sup><sup>σ</sup>

CA, T <sup>¼</sup> <sup>M</sup><sup>σ</sup>

<sup>f</sup> � <sup>M</sup><sup>0</sup> s

<sup>s</sup> � <sup>M</sup><sup>0</sup> s

> <sup>f</sup> � <sup>M</sup><sup>0</sup> s

<sup>s</sup> ð Þ K 324 EAð Þ MPa 72,000

<sup>f</sup> ð Þ K 311 EMð Þ MPa 70,000

<sup>s</sup> (K) 330 ε<sup>0</sup> 0.023937

<sup>f</sup> (K) 340 H(MPa) 0.2606751918

<sup>f</sup> , f ¼ 1 (20)

Modeling of the Two-Way Shape Memory Effect http://dx.doi.org/10.5772/intechopen.75657 47

� � � <sup>C</sup> � <sup>K</sup> � <sup>H</sup> <sup>¼</sup> 0 (21)

<sup>s</sup> , f ¼ 1 (22)

� � � <sup>C</sup> <sup>þ</sup> <sup>K</sup> <sup>þ</sup> <sup>H</sup> <sup>¼</sup> 0 (23)

<sup>f</sup> , f ¼ 0 (24)

� � <sup>þ</sup> <sup>C</sup> <sup>þ</sup> <sup>H</sup> <sup>¼</sup> 0 (25)

$$\boldsymbol{\phi}^{\text{di}}(\sigma = \sigma\_{00}, T, f) = \varepsilon\_{0}. \sigma\_{00} : \boldsymbol{R} - \boldsymbol{B}. \left(T - \boldsymbol{M}\_{s}^{0}\right) + \boldsymbol{\mathcal{C}}(2f - 1) - \boldsymbol{K}f - \boldsymbol{H} \tag{8}$$

Condition of consistence gives

$$d\boldsymbol{\phi}^{\rm di}(\boldsymbol{\sigma} = \boldsymbol{\sigma}\_{00}, \mathbf{T}, \mathbf{f}) = 0; \dot{\mathbf{f}} > 0; \mathbf{f} \ge 0 \; ; \mathbf{f} \le \mathbf{1} \tag{9}$$

$$\frac{\partial \boldsymbol{\phi}^{\rm di}}{\partial \boldsymbol{\sigma}} d\boldsymbol{\sigma} + \frac{\partial \boldsymbol{\phi}^{\rm di}}{\partial T} \boldsymbol{\text{d}T} + \frac{\partial \boldsymbol{\phi}^{\rm di}}{\partial \boldsymbol{f}} \boldsymbol{\text{d}f} = \boldsymbol{0} \ (d\boldsymbol{\sigma} = \boldsymbol{0}) \tag{10}$$

$$\text{pdf} = \frac{\text{B.dT}}{(\text{2C} - \text{K})} ; \dot{\text{f}} > 0 \tag{11}$$

Doing the same with the reverse transformation

$$\boldsymbol{\phi}^{\rm in}(\boldsymbol{\sigma} = \boldsymbol{\sigma}\_{00}, T, \boldsymbol{f}) = \boldsymbol{\varepsilon}\_{0}.\\\sigma\_{00} : \boldsymbol{R} - \boldsymbol{B}. \left(\boldsymbol{T} - \boldsymbol{M}\_{s}^{0}\right) + \boldsymbol{\mathcal{C}}(\boldsymbol{2}\boldsymbol{f} - \boldsymbol{1}) + \boldsymbol{\mathcal{G}}\boldsymbol{f} + \boldsymbol{H} \tag{12}$$

$$\text{pdf} = \frac{\text{B.dT}}{(\text{2C} + \text{K})}; \dot{\text{f}} < 0; \text{f} \ge 0 \; ; \text{f} \le 1 \tag{13}$$

Eqs. (11) and (13) give the evolution of fraction of martensite.

The deformation resulting from transformation of austenite to martensite is denoted ε<sup>T</sup>; this deformation is associated with fraction of martensite:

$$\mathbf{d}\boldsymbol{\varepsilon}^{\mathrm{T}} = \mathbf{d}\mathbf{f}.\varepsilon\_{0}.\mathbf{R};\dot{\mathbf{f}} > 0; \mathbf{f} \ge 0 \; ; \mathbf{f} \le 1\tag{14}$$

R is a tensor of transformation, and it can be written as the following:

$$R = \frac{\sigma}{\sqrt{\sigma \cdot \sigma}}\tag{15}$$

$$\mathbf{d}\,\mathbf{d}\,\boldsymbol{\varepsilon}^{\mathrm{T}} = \frac{\mathbf{B}.\mathbf{d}\mathbf{T}}{(\mathbf{2C} - \mathbf{K})} \varepsilon\_{0}.\mathbf{R}; \dot{\mathbf{f}} > 0; \mathbf{f} \ge 0 \; ; \mathbf{f} \le 1\tag{16}$$

$$\mathbf{d}\,\varepsilon^{\mathrm{T}} = \frac{\mathbf{B}\,\mathrm{d}\mathbf{T}}{(2\mathbf{C} + \mathbf{K})} \varepsilon\_{0}.\mathbf{R}; \mathbf{\dot{f}} < 0; \mathbf{f} \ge 0 \; ; \mathbf{f} \le 1\tag{17}$$

#### 2.2. Determination of constants B, C, K, and H

At the beginning of direct transformation

$$
\sigma\_{00} = \begin{pmatrix} \sigma\_0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}, T = M\_{s\prime}^{\sigma} f = 0 \tag{18}
$$

$$\varphi^{\rm di}\left(\sigma = \sigma\_{00}, T = M\_s^\circ, f = 0\right) = \varepsilon\_0.\sigma\_{00} : R - B.\left(M\_s^\circ - M\_s^0\right) + \mathcal{C} - H = 0 \tag{19}$$

At the end of the direct transformation

<sup>φ</sup>di <sup>¼</sup> Fth � Fdi; \_

<sup>d</sup>φdið Þ¼ <sup>σ</sup> <sup>¼</sup> <sup>σ</sup>00; <sup>T</sup>; <sup>f</sup> <sup>0</sup>; \_

∂φdi <sup>∂</sup><sup>T</sup> dT <sup>þ</sup>

df <sup>¼</sup> <sup>B</sup>:dT

ð Þ 2C <sup>þ</sup> <sup>K</sup> ; \_

<sup>φ</sup>dið Þ¼ <sup>σ</sup> <sup>¼</sup> <sup>σ</sup>00; <sup>T</sup>; <sup>f</sup> <sup>ε</sup>0:σ<sup>00</sup> : <sup>R</sup> � <sup>B</sup>: <sup>T</sup> � <sup>M</sup><sup>0</sup>

∂φdi ∂σ

Doing the same with the reverse transformation

dσ þ

<sup>φ</sup>inð Þ¼ <sup>σ</sup> <sup>¼</sup> <sup>σ</sup>00; <sup>T</sup>; <sup>f</sup> <sup>ε</sup>0:σ<sup>00</sup> : <sup>R</sup> � <sup>B</sup>: <sup>T</sup> � <sup>M</sup><sup>0</sup>

Eqs. (11) and (13) give the evolution of fraction of martensite.

deformation is associated with fraction of martensite:

2.2. Determination of constants B, C, K, and H

<sup>φ</sup>di <sup>σ</sup> <sup>¼</sup> <sup>σ</sup>00; <sup>T</sup> <sup>¼</sup> <sup>M</sup><sup>σ</sup>

At the beginning of direct transformation

df <sup>¼</sup> <sup>B</sup>:dT

<sup>d</sup>ε<sup>T</sup> <sup>¼</sup> df:ε0:R; \_

R is a tensor of transformation, and it can be written as the following:

<sup>d</sup>ε<sup>T</sup> <sup>¼</sup> <sup>B</sup>:dT

<sup>d</sup>ε<sup>T</sup> <sup>¼</sup> <sup>B</sup>:dT

σ<sup>00</sup> ¼

0 B@

<sup>s</sup> ; <sup>f</sup> <sup>¼</sup> <sup>0</sup> � � <sup>¼</sup> <sup>ε</sup>0:σ<sup>00</sup> : <sup>R</sup> � <sup>B</sup>: <sup>M</sup><sup>σ</sup>

Condition of consistence gives

46 Shape-Memory Materials

f > 0; f ≥ 0 ; f ≤ 1 (7)

� � <sup>þ</sup> <sup>C</sup>ð Þ� <sup>2</sup><sup>f</sup> � <sup>1</sup> Kf � <sup>H</sup> (8)

f > 0; f ≥ 0 ;f ≤ 1 (9)

<sup>∂</sup><sup>f</sup> df <sup>¼</sup> <sup>0</sup> ð Þ <sup>d</sup><sup>σ</sup> <sup>¼</sup> <sup>0</sup> (10)

� � <sup>þ</sup> <sup>C</sup>ð Þþ <sup>2</sup><sup>f</sup> � <sup>1</sup> Gf <sup>þ</sup> <sup>H</sup> (12)

f < 0; f ≥ 0 ; f ≤ 1 (13)

f > 0; f ≥ 0 ; f ≤ 1 (14)

<sup>σ</sup>:<sup>σ</sup> <sup>p</sup> (15)

f > 0; f ≥ 0 ;f ≤ 1 (16)

f < 0; f ≥ 0 ;f ≤ 1 (17)

<sup>s</sup> , f ¼ 0 (18)

� � <sup>þ</sup> <sup>C</sup> � <sup>H</sup> <sup>¼</sup> 0 (19)

f > 0 (11)

s

s

∂φdi

ð Þ 2C � <sup>K</sup> ; \_

The deformation resulting from transformation of austenite to martensite is denoted ε<sup>T</sup>; this

<sup>R</sup><sup>¼</sup> <sup>σ</sup> ffiffiffiffiffiffiffi

ð Þ 2C � <sup>K</sup> <sup>ε</sup>0:R; \_

ð Þ 2C <sup>þ</sup> <sup>K</sup> <sup>ε</sup>0:R; \_

1

CA, T <sup>¼</sup> <sup>M</sup><sup>σ</sup>

<sup>s</sup> � <sup>M</sup><sup>0</sup> s

$$
\sigma\_{00} = \begin{pmatrix} \sigma\_0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}, T = M\_{f'}^\circ f = 1 \tag{20}
$$

$$\rho^{\rm di}\left(\sigma = \sigma\_0, T = M\_f^{\sigma}, f = 1\right) = \varepsilon\_0.\sigma\_0: R - B.\left(M\_f^{\sigma} - M\_s^0\right) - \mathbb{C} - K - H = 0\tag{21}$$

At the beginning of the reverse transformation

$$
\sigma\_{00} = \begin{pmatrix} \sigma\_0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}, T = A\_{s'}^{\sigma} f = 1 \tag{22}
$$

$$\boldsymbol{\varrho}^{\rm in} \left( \boldsymbol{\sigma} = \boldsymbol{\sigma}\_{0}, \boldsymbol{T} = A\_{\rm s}^{\boldsymbol{\sigma}}, \boldsymbol{f} = 1 \right) = \boldsymbol{\varepsilon}\_{0}.\\\boldsymbol{\sigma}\_{0} : \boldsymbol{R} - B. \left( A\_{\rm s}^{\boldsymbol{\sigma}} - M\_{\rm s}^{0} \right) - \boldsymbol{\mathcal{C}} + \boldsymbol{K} + \boldsymbol{H} = \boldsymbol{0} \tag{23}$$

At the end of the reverse transformation

$$
\sigma\_{00} = \begin{pmatrix} \sigma\_0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}, \\
 T = A^{\sigma}\_{f'} f = 0 \tag{24}
$$

$$\phi^{in}\left(\sigma = \sigma\_0, T = A^{\sigma}\_f, f = 0\right) = \varepsilon\_0.\sigma\_0: R - B.\left(A^{\sigma}\_f - M^0\_s\right) + \mathcal{C} + H = 0\tag{25}$$

#### 2.3. Experimental data

Table 1 illustrates experimental data and material constants B, C, K, and H. The used material is CuZnAl. The test was performed under constant stress (σ ¼ 65 MPa).

#### 2.4. Numerical simulation

#### 2.4.1. One-dimensional case

We considered a segment of CuZnAl submitted to a constant stress (σ ¼ 65 MPa) and a thermal load (300 ≤ T ≤ 400 K) (Figure 3).


Table 1. Experimental data [8, 11].

#### 2.4.2. Three-dimensional case

The considered specimen is a cubic element subjected to a constant mechanical load which is a triaxial traction and thermal loads (σ<sup>11</sup> ¼ σ<sup>22</sup> ¼ σ<sup>33</sup> ¼ 50 MPa) and (300 ≤ T ≤ 400 K) (Figures 4–6).

Figure 5. Loading in the direction of σ22.

Modeling of the Two-Way Shape Memory Effect http://dx.doi.org/10.5772/intechopen.75657 49

Figure 6. Loading in the direction of σ33.

Figure 3. History of coupled loading.

Figure 4. Loading in the direction of σ11.

Figure 5. Loading in the direction of σ22.

2.4.2. Three-dimensional case

Figure 3. History of coupled loading.

Figure 4. Loading in the direction of σ11.

(Figures 4–6).

48 Shape-Memory Materials

The considered specimen is a cubic element subjected to a constant mechanical load which is a triaxial traction and thermal loads (σ<sup>11</sup> ¼ σ<sup>22</sup> ¼ σ<sup>33</sup> ¼ 50 MPa) and (300 ≤ T ≤ 400 K)

Figure 6. Loading in the direction of σ33.

## 3. Results

#### 3.1. One-dimensional case

3.2. Three-dimensional case

Modeling of the Two-Way Shape Memory Effect http://dx.doi.org/10.5772/intechopen.75657 51

Figure 9. Plot Tε11.

Figure 10. Plot T ε22.

Figure 7. Response at (σ ¼ 65 MPa).

Figure 8. Evolution of the fraction of martensite.

#### 3.2. Three-dimensional case

3. Results

50 Shape-Memory Materials

3.1. One-dimensional case

Figure 7. Response at (σ ¼ 65 MPa).

Figure 8. Evolution of the fraction of martensite.

Figure 9. Plot Tε11.

Figure 10. Plot T ε22.

4. Discussion

has permitted to obtain previous results.

Figure 13. Evolution of fraction of martensite in reverse transformation.

behaves well in one-dimensional case.

due to the triaxial loading.

thermal load; for each plot, there is a hysteresis.

case of one-dimensional two-way effect (Figure 7).

After having written constitutive equations and criteria functions, the numerical simulation

Modeling of the Two-Way Shape Memory Effect http://dx.doi.org/10.5772/intechopen.75657 53

First, we used the extracted values from the curve of the test in order to compare this curve with the response of the model in one-dimensional case, and we obtained Figure 7. This figure

On the other hand, Figure 8, which is representing the evolution of the martensite fraction, is also in agreement with the curve in Figure 7, i.e., the direct transformation and the reverse transformation are functions of martensite fraction. We can say that the constitutive model

For the three-dimensional case, Figures 9–11 show the response under the triaxial traction and

The shrinking of the hysteresis in each case of the figures should be noted (Figures 9–11); this is

Despite the applied triaxial load, Figures 9–11 exhibit the thermomechanical cycle as it is in

Figures 12 and 13 show the evolution of fraction of martensite for each case of direct and reverse transformations, and the shapes of the plots are compatible with Figures 9–11 as the

presents a good agreement between experimental data and the model response.

Figure 11. Plot Tε22.

Figure 12. Evolution of fraction of martensite in direct transformation.

Figure 13. Evolution of fraction of martensite in reverse transformation.

## 4. Discussion

Figure 11. Plot Tε22.

52 Shape-Memory Materials

Figure 12. Evolution of fraction of martensite in direct transformation.

After having written constitutive equations and criteria functions, the numerical simulation has permitted to obtain previous results.

First, we used the extracted values from the curve of the test in order to compare this curve with the response of the model in one-dimensional case, and we obtained Figure 7. This figure presents a good agreement between experimental data and the model response.

On the other hand, Figure 8, which is representing the evolution of the martensite fraction, is also in agreement with the curve in Figure 7, i.e., the direct transformation and the reverse transformation are functions of martensite fraction. We can say that the constitutive model behaves well in one-dimensional case.

For the three-dimensional case, Figures 9–11 show the response under the triaxial traction and thermal load; for each plot, there is a hysteresis.

The shrinking of the hysteresis in each case of the figures should be noted (Figures 9–11); this is due to the triaxial loading.

Despite the applied triaxial load, Figures 9–11 exhibit the thermomechanical cycle as it is in case of one-dimensional two-way effect (Figure 7).

Figures 12 and 13 show the evolution of fraction of martensite for each case of direct and reverse transformations, and the shapes of the plots are compatible with Figures 9–11 as the one-dimensional case because it was noticed previously that the deformation is proportional to the amount of martensite.

[4] Otsuka K. Perspective of research on martensitic transformations present and future.

Modeling of the Two-Way Shape Memory Effect http://dx.doi.org/10.5772/intechopen.75657 55

[5] J. Van Humbeeck. La transformation martensitique, dans Technologie des. Chapter 3. In:

[6] Duerig T, Pelton A, Stockel D. An overview of nitinol medical applications. Materials

[7] Miller DA, Lagoudas DC. Thermo-mechanical characterization of NiTiCu and NiTi SMA actuators: Influence of plastic strains. Smart Materials and Structures. 2000;9(5):640-652 [8] Bourbon G, Lexcellent C, Leclercq S. Modelling of the non-isothermal cyclic behaviour of a polycrystalline Cu-Zn-Al shape memory alloy. Journal de Physique IV. 1995;5(C8):221-

[9] Patoor E, Eberhardt A, Berveiller M. On Micromechanics of Thermoelastic Phase Transition. The proceedings of Plasticity 93: The Fourth International Symposium on Plasticity

[10] Lagoudas DC, Entchev PB. Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: Constitutive model for fully dense

[11] Shape Memory Applications Inc. Available from: http://heim.ifi.uio.no/~mes/inf1400/

COOL/Robot%20Prosjekt/Flexinol/Shape%20Memory%20Alloys.htm

Alliages 'a M'emoire de Forme. Paris, France: Hermes; 1993. pp. 63-88

Journal de Physique IV. 2001;11:3-9

226

Science and Engineering. 1999;A273-275:149-160

and Its Applications, Baltimore, Maryland. 1993, July. 19-23

SMAs. Mechanics of Materials. 2004;36(9):865-892

## 5. Conclusion

In this work, we have developed a 3D constitutive model using the principles of thermodynamics and a simple formalism, and these principles have permitted to write criteria of transformation. This macroscopic model is developed by simple formalism and assumptions.

By using an algorithm, we have implemented the model, and the response seems to be compatible with the nature of the two-way shape memory effect. In the one-dimensional case, we have observed a good agreement between the numerical and experimental plots.

It should be noted that the parameters of the model were determined by the one-dimensional test and further used in the biaxial and triaxial cases to ensure consistency of the model in different cases of loading. The implementation of the model in the algorithm is simple and practical. The obtained results testify the usability of the developed model.

At the end, we can say that this macroscopic constitutive model can be used in applications to engineering problems, in order to particularly simulate the pseudoelastic effect of shape memory alloys.

## Author details

Meddour Belkacem\* and Brek Samir

\*Address all correspondence to: samsum66@gmail.com.in

Department of Mechanical Engineering, University of Khenchela, Algeria

## References


[4] Otsuka K. Perspective of research on martensitic transformations present and future. Journal de Physique IV. 2001;11:3-9

one-dimensional case because it was noticed previously that the deformation is proportional to

In this work, we have developed a 3D constitutive model using the principles of thermodynamics and a simple formalism, and these principles have permitted to write criteria of transformation. This macroscopic model is developed by simple formalism and assumptions. By using an algorithm, we have implemented the model, and the response seems to be compatible with the nature of the two-way shape memory effect. In the one-dimensional case,

It should be noted that the parameters of the model were determined by the one-dimensional test and further used in the biaxial and triaxial cases to ensure consistency of the model in different cases of loading. The implementation of the model in the algorithm is simple and

At the end, we can say that this macroscopic constitutive model can be used in applications to engineering problems, in order to particularly simulate the pseudoelastic effect of shape

[1] Arghavani J, Auricchio F, Naghdabadi R, Reali A, Sohrabpour S. A 3D phenomenological constitutive model for shape memory alloys under multiaxial loadings. International

[2] Yutaka T, Jong-Bin L, Minoru T. Finite element analysis of superelastic, large deformation behaviour of shape memory alloy helical springs. Computers and Structures. 2004;82:

[3] Pan H, Thamburaja P, Chau FS. Multi-axial behaviour of shape memory alloys undergoing martensitic reorientation and detwinning. International Journal of Plasticity. 2007;23:

we have observed a good agreement between the numerical and experimental plots.

practical. The obtained results testify the usability of the developed model.

Department of Mechanical Engineering, University of Khenchela, Algeria

the amount of martensite.

5. Conclusion

54 Shape-Memory Materials

memory alloys.

Author details

References

1685-1693

711-732

Meddour Belkacem\* and Brek Samir

\*Address all correspondence to: samsum66@gmail.com.in

Journal of Plasticity. 2010;26:976-991


**Chapter 4**

Provisional chapter

**Linear Shape Memory Alloy Thermomechanical**

DOI: 10.5772/intechopen.76292

The thermally activated changes in crystal structure in nickel-titanium shape memory alloy (SMA) material, which produces transformation strains of an order of magnitude higher than and opposite to the thermal strains, have been described using different models. Some of these models are defined by cyclic functions (trigonometric functions) which they become complex to control when they are subjected to a wide range of transformation temperatures. This chapter presents an alternative model to better describe the behavior of SMA for a more general temperature range, which an SMA-powered actuator might be subjected to. The proposed model is then implemented to the analysis of one-dimensional (1D) problem oriented to the two-dimensional (2D) space. The simu-

Keywords: shape memory alloy, finite element analysis, shape memory effect, phase

Shape memory alloys (SMAs) are being described as smart materials due to their ability of memorizing shape. Their ability in memorizing shapes requires some training suitable for user's application. The trained SMA exhibits two behaviors, that is, superelasticity and shape memory effect depending on the temperature. Those behaviors are triggered by the phenomenon occurring at the microstructural level called phase transformation. Phase transformation can be induced by stress or temperature. When SMA is mechanically loaded at room temperature (or at a temperature below thermal transition), the twinned martensite transforms to detwinned martensite [1]. When the detwinned martensite is subjected to heat, the detwinned martensite transforms to austenite phase. When the fully austenite SMA is cooled down, there

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

lation results were then graphically compared to the experiment.

Linear Shape Memory Alloy Thermomechanical

**Actuators**

Abstract

transformation

1. Introduction

Actuators

Velaphi Msomi and Graeme Oliver

Velaphi Msomi and Graeme Oliver

http://dx.doi.org/10.5772/intechopen.76292

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Linear Shape Memory Alloy Thermomechanical Actuators** Linear Shape Memory Alloy Thermomechanical Actuators

DOI: 10.5772/intechopen.76292

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76292

Velaphi Msomi and Graeme Oliver

Velaphi Msomi and Graeme Oliver

#### Abstract

The thermally activated changes in crystal structure in nickel-titanium shape memory alloy (SMA) material, which produces transformation strains of an order of magnitude higher than and opposite to the thermal strains, have been described using different models. Some of these models are defined by cyclic functions (trigonometric functions) which they become complex to control when they are subjected to a wide range of transformation temperatures. This chapter presents an alternative model to better describe the behavior of SMA for a more general temperature range, which an SMA-powered actuator might be subjected to. The proposed model is then implemented to the analysis of one-dimensional (1D) problem oriented to the two-dimensional (2D) space. The simulation results were then graphically compared to the experiment.

Keywords: shape memory alloy, finite element analysis, shape memory effect, phase transformation

## 1. Introduction

Shape memory alloys (SMAs) are being described as smart materials due to their ability of memorizing shape. Their ability in memorizing shapes requires some training suitable for user's application. The trained SMA exhibits two behaviors, that is, superelasticity and shape memory effect depending on the temperature. Those behaviors are triggered by the phenomenon occurring at the microstructural level called phase transformation. Phase transformation can be induced by stress or temperature. When SMA is mechanically loaded at room temperature (or at a temperature below thermal transition), the twinned martensite transforms to detwinned martensite [1]. When the detwinned martensite is subjected to heat, the detwinned martensite transforms to austenite phase. When the fully austenite SMA is cooled down, there

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

will be a temperature range where austenite will transform back to twinned martensite. This whole process is called shape memory effect. When a mechanical load is applied on SMA which is subjected to temperature above austenitic finish temperature, the deformation will take place. The deformation will be reversed completely upon the removal of mechanical load. This phenomenon is called superelasticity. These two physical behaviors are the ones that make SMA a good candidate for actuation applications. There are a number of models reported in the study which are meant to describe the phase transformation kinetics [1]. The first model was developed by Tanaka and Nagaki [2, 3] which was later improved by Boyd and Lagoudas [4]. The firstly developed model was based on exponential functions. Boyd and Lagoudas redefined the material constants so as to suit their application. Later, a model based on cosine functions was developed by Liang and Rogers [5]. Liang and Rogers developed their model with the purpose of applying it to the analysis of acoustic vibrations control [5–7]. The common factor in these models is the calculation material constants which are calculated based on transformation temperatures. Brinson [8] developed another alternative phase transformation model, where the internal variable measuring the evolution of martensite phase was split into two.

material constants and austenite start temperature, respectively. Boyd and Lagoudas [11]

Later, Liang and Rogers [5] presented another alternative model for martensite volume fraction calculation. Their model was based on trigonometric functions (cyclic functions), that is, cosine functions. The following equation describes the phase transformation during heating

<sup>2</sup> <sup>1</sup> <sup>þ</sup> cos AA <sup>T</sup> � As � <sup>σ</sup>

The transformation occurs during cooling (austenite transforms to martensite) and is given by

CMð Þ T � Ms < σ < CM T � Mf

The material constants involved in Liang and Rogers [5] are the same as those used in Tanaka's model [2]. The difference comes with the calculation of the two constants which are given as

It should be noted that the calculation of the two material constants, AA and AM, involves the difference in transformation temperatures. It was noticed that the previously mentioned models were not compatible with our application due to the size of our temperature range. The new non-cyclic model had to be developed. The proposed phase transformation model is based on the hyperbolic functions. The phase transformation during heating (martensite trans-

The phase transformation during cooling (austenite transforms to martensite) is described by

ξ ¼ ξ<sup>0</sup> 1 � tanh AM T � Mf

; AA <sup>¼</sup> <sup>π</sup>

Af � As

ξ ¼ ξ0f g 1 � tanh½ � AAð Þþ T � As ϑ<sup>A</sup> (9)

(10)

<sup>þ</sup> <sup>ϑ</sup><sup>M</sup>

<sup>2</sup> cos AM <sup>T</sup> � Mf � <sup>σ</sup>

, aA <sup>¼</sup> 2ln10 Af � As

CA

CM

(4)

<sup>&</sup>lt; <sup>σ</sup> <sup>&</sup>lt; CAð Þ <sup>T</sup> � As (5)

þ 1 þ ξ<sup>0</sup>

<sup>2</sup> (6)

(7)

, bA <sup>¼</sup> aA CA

Linear Shape Memory Alloy Thermomechanical Actuators

http://dx.doi.org/10.5772/intechopen.76292

(3)

59

(8)

developed the calculation of material constants (aM, bM, aA and bA) as follows:

, bM <sup>¼</sup> aM CM

aM <sup>¼</sup> 2ln10 Ms � Mf

<sup>ξ</sup> <sup>¼</sup> <sup>ξ</sup><sup>0</sup>

<sup>ξ</sup> <sup>¼</sup> <sup>1</sup> � <sup>ξ</sup><sup>0</sup>

forms to austenite) is given by the following equation:

The stress restriction is described as follows:

follows:

the following equation:

This transformation occurs between the stress ranges described as follows:

CA T � Af

AM <sup>¼</sup> <sup>π</sup>

Ms � Mf

(martensite transforms to austenite):

The first internal variable is induced by temperature and the second one is induced by stress. This work proposed that the elastic modulus should be split into austenitic and martensitic modulus. It should be noted that these models developed by the previously listed authors are functions of transformation temperature (martensite start temperature, martensite finish temperature, austenite start temperature and austenite finish temperature). These temperatures are crucial since they are used to calculate certain material constants. More work has been done in improving the already existing models [9, 12–15]. This chapter proposes a one-dimensional (1D) new model to describe the physical behavior of SMA for all transformation ranges. The proposed model is then used to simulate 1D structural deflection which is orientated in twodimensional (2D) space. The simulated results are compared to the experimental results.

## 2. Phase transformation models

This section shows the already available phase transformation models. It should be noted that the law adopted for the proposed model is based on the one adopted by Liang and Rogers [5] with the difference on the phase transformation estimation. The first phase transformation model based on exponential functions was developed by Tanaka et al. [2, 3]. The transformation from martensite to austenite is given by

$$\xi = \xi\_0 \exp[a\_A(T - A\_s) - b\_A \sigma] \tag{1}$$

And the transformation from austenite to martensite is given by

$$\xi = 1 - \exp[a\_M(T - M\_s) - b\_M \sigma] + \xi\_0 \tag{2}$$

where ξ0, aM and bM, Ms, σ, aA, bA and As are internal variables measuring martensite volume fraction evolution, martensitic material constants, martensite start temperature, austenitic material constants and austenite start temperature, respectively. Boyd and Lagoudas [11] developed the calculation of material constants (aM, bM, aA and bA) as follows:

$$a\_M = \frac{2\ln 10}{M\_s - M\_f}, b\_M = \frac{a\_M}{\mathbb{C}\_M}, a\_A = \frac{2\ln 10}{A\_f - A\_s}, b\_A = \frac{a\_A}{\mathbb{C}\_A} \tag{3}$$

Later, Liang and Rogers [5] presented another alternative model for martensite volume fraction calculation. Their model was based on trigonometric functions (cyclic functions), that is, cosine functions. The following equation describes the phase transformation during heating (martensite transforms to austenite):

$$\xi = \frac{\xi\_0}{2} \left\{ 1 + \cos \left[ A\_A \left( T - A\_s - \frac{\sigma}{C\_A} \right) \right] \right\} \tag{4}$$

This transformation occurs between the stress ranges described as follows:

$$
\mathbb{C}\_A \left( T - A\_f \right) < \sigma < \mathbb{C}\_A (T - A\_s) \tag{5}
$$

The transformation occurs during cooling (austenite transforms to martensite) and is given by

$$\xi = \frac{1 - \xi\_0}{2} \cos \left[ A\_M \left( T - M\_f - \frac{\sigma}{\mathbb{C}\_M} \right) \right] + \frac{1 + \xi\_0}{2} \tag{6}$$

The stress restriction is described as follows:

will be a temperature range where austenite will transform back to twinned martensite. This whole process is called shape memory effect. When a mechanical load is applied on SMA which is subjected to temperature above austenitic finish temperature, the deformation will take place. The deformation will be reversed completely upon the removal of mechanical load. This phenomenon is called superelasticity. These two physical behaviors are the ones that make SMA a good candidate for actuation applications. There are a number of models reported in the study which are meant to describe the phase transformation kinetics [1]. The first model was developed by Tanaka and Nagaki [2, 3] which was later improved by Boyd and Lagoudas [4]. The firstly developed model was based on exponential functions. Boyd and Lagoudas redefined the material constants so as to suit their application. Later, a model based on cosine functions was developed by Liang and Rogers [5]. Liang and Rogers developed their model with the purpose of applying it to the analysis of acoustic vibrations control [5–7]. The common factor in these models is the calculation material constants which are calculated based on transformation temperatures. Brinson [8] developed another alternative phase transformation model, where the

internal variable measuring the evolution of martensite phase was split into two.

2. Phase transformation models

58 Shape-Memory Materials

tion from martensite to austenite is given by

And the transformation from austenite to martensite is given by

The first internal variable is induced by temperature and the second one is induced by stress. This work proposed that the elastic modulus should be split into austenitic and martensitic modulus. It should be noted that these models developed by the previously listed authors are functions of transformation temperature (martensite start temperature, martensite finish temperature, austenite start temperature and austenite finish temperature). These temperatures are crucial since they are used to calculate certain material constants. More work has been done in improving the already existing models [9, 12–15]. This chapter proposes a one-dimensional (1D) new model to describe the physical behavior of SMA for all transformation ranges. The proposed model is then used to simulate 1D structural deflection which is orientated in twodimensional (2D) space. The simulated results are compared to the experimental results.

This section shows the already available phase transformation models. It should be noted that the law adopted for the proposed model is based on the one adopted by Liang and Rogers [5] with the difference on the phase transformation estimation. The first phase transformation model based on exponential functions was developed by Tanaka et al. [2, 3]. The transforma-

where ξ0, aM and bM, Ms, σ, aA, bA and As are internal variables measuring martensite volume fraction evolution, martensitic material constants, martensite start temperature, austenitic

ξ ¼ ξ<sup>0</sup> exp½ � aAð Þ� T � As bAσ (1)

ξ ¼ 1 � exp½aMð Þ� T � Ms bMσ� þ ξ<sup>0</sup> (2)

$$\mathbb{C}\_{M}(T - M\_{s}) < \sigma < \mathbb{C}\_{M}(T - M\_{f}) \tag{7}$$

The material constants involved in Liang and Rogers [5] are the same as those used in Tanaka's model [2]. The difference comes with the calculation of the two constants which are given as follows:

$$A\_M = \frac{\pi}{M\_s - M\_f}; A\_A = \frac{\pi}{A\_f - A\_s} \tag{8}$$

It should be noted that the calculation of the two material constants, AA and AM, involves the difference in transformation temperatures. It was noticed that the previously mentioned models were not compatible with our application due to the size of our temperature range. The new non-cyclic model had to be developed. The proposed phase transformation model is based on the hyperbolic functions. The phase transformation during heating (martensite transforms to austenite) is given by the following equation:

$$\xi = \xi\_0 \{ 1 - \tanh[A\_A(T - A\_s) + \mathfrak{G}\_A] \} \tag{9}$$

The phase transformation during cooling (austenite transforms to martensite) is described by the following equation:

$$\xi = \xi\_0 \left\{ 1 - \tanh\left[ A\_M (T - M\_f) + \mathfrak{d}\_M \right] \right\} \tag{10}$$

The calculation of material constants AA and AM is similar to that of Eq. (8). The phase transformation constants (As and Ms) are those described previously. The constants ϑ<sup>A</sup> and ϑ<sup>M</sup> are given by

$$\mathfrak{G}\_A = -\frac{A\_A}{\mathbb{C}\_A}\sigma; \mathfrak{G}\_M = -\frac{A\_M}{\mathbb{C}\_M}\sigma \tag{11}$$

of the wire increased from the room temperature to a maximum temperature. The wire was allowed to cool down after reaching the maximum deflection of the beam, and then the beam could go back to its rest position. This process was repeated several times so as to get stable

Linear Shape Memory Alloy Thermomechanical Actuators

http://dx.doi.org/10.5772/intechopen.76292

61

The following figures show the experimental results for the beam deflection test and these results are used to validate FEA results. Although there were several tests conducted, only one graph is presented to avoid repetition. It should be noted that the results presented are already translated into millimeters using the method explained in the study [10]. Figure 2 shows the time it takes for a beam to finish the full deflection cycle, that is, the deflection from the rest position to the final position or the maximum deflection and from the final position back to the

During heating, the beam deflects from the rest position to the maximum deflection and the reverse during cooling. It is clearly seen from the figure that the beam's maximum deflection is reached in less than 10 s which is very quick. This quickness is suggested to be related to the wire diameter. The smaller the diameter, the faster the response of the wire. It is noted in

results.

rest position.

4. Deflection test results

Figure 1. Beam test experiment setup.

The constants CA and CM are the same as those used by Liang and Rogers. The developed phase transformation model was then used in performing the 2D analysis on a steel beam deflection explained in the next section. Prior to the performance of simulation analysis, an experiment was performed with the purpose of obtaining simulation parameters and verification of numerical results.

## 3. Beam deflection test experiment

The experiment was performed using the following equipment:


The steel beam used in the performance of this experiment was 300-mm long with a 25-mm breadth and 1.2-mm thickness. Both ends of the steel beam were fixed on top of the vertical rectangular steel frame. The effective length for the steel beam after installation to the vertical rectangular steel frame was 243 mm. Figure 1 shows the complete experimental setup.

A 184-mm long NiTi SMA wire with a 0.5-mm diameter was attached with one end at the center of the steel beam and the other end at the center foot of the steel frame. The attachment of the NiTi SMA wire to the frame and to the beam was isolated using high-melting temperature plastic tubes. The isolation was required since the NiTi SMA wire was heated through the joules heating method. The NiTi SMA wire was attached at the center of the beam so as to get the maximum deflection. During the performance of the experiment, two types of data were being logged, that is, beam deflection and the NiTi SMA wire temperature. The beam deflection was recorded through the LVDT which was powered by the DC power supply (shown in Figure 1). The LVDT data were logged in the form of output voltage and it was translated into millimeters using the method described subsequently. The temperature was recorded using a GLX explorer data logger. A 1.54 A was supplied to the NiTi SMA wire, and the temperature

Figure 1. Beam test experiment setup.

The calculation of material constants AA and AM is similar to that of Eq. (8). The phase transformation constants (As and Ms) are those described previously. The constants ϑ<sup>A</sup> and ϑ<sup>M</sup> are

The constants CA and CM are the same as those used by Liang and Rogers. The developed phase transformation model was then used in performing the 2D analysis on a steel beam deflection explained in the next section. Prior to the performance of simulation analysis, an experiment was performed with the purpose of obtaining simulation parameters and verifica-

The steel beam used in the performance of this experiment was 300-mm long with a 25-mm breadth and 1.2-mm thickness. Both ends of the steel beam were fixed on top of the vertical rectangular steel frame. The effective length for the steel beam after installation to the vertical

A 184-mm long NiTi SMA wire with a 0.5-mm diameter was attached with one end at the center of the steel beam and the other end at the center foot of the steel frame. The attachment of the NiTi SMA wire to the frame and to the beam was isolated using high-melting temperature plastic tubes. The isolation was required since the NiTi SMA wire was heated through the joules heating method. The NiTi SMA wire was attached at the center of the beam so as to get the maximum deflection. During the performance of the experiment, two types of data were being logged, that is, beam deflection and the NiTi SMA wire temperature. The beam deflection was recorded through the LVDT which was powered by the DC power supply (shown in Figure 1). The LVDT data were logged in the form of output voltage and it was translated into millimeters using the method described subsequently. The temperature was recorded using a GLX explorer data logger. A 1.54 A was supplied to the NiTi SMA wire, and the temperature

rectangular steel frame was 243 mm. Figure 1 shows the complete experimental setup.

<sup>σ</sup>; <sup>ϑ</sup><sup>M</sup> ¼ � AM

CM

σ (11)

<sup>ϑ</sup><sup>A</sup> ¼ � AA CA

given by

60 Shape-Memory Materials

tion of numerical results.

1. Explorer GLX Data logger

5. Fluke 190C Scope meter 6. Rectangular steel beam 7. Rectangular steel frame

3. Beam deflection test experiment

The experiment was performed using the following equipment:

2. Nickel titanium shape memory alloy wire of 0.5-mm diameter

3. ISO-TECH IPS 2303 Laboratory DC Power Supply

4. Linear variable differential transformer (LVDT)

of the wire increased from the room temperature to a maximum temperature. The wire was allowed to cool down after reaching the maximum deflection of the beam, and then the beam could go back to its rest position. This process was repeated several times so as to get stable results.

## 4. Deflection test results

The following figures show the experimental results for the beam deflection test and these results are used to validate FEA results. Although there were several tests conducted, only one graph is presented to avoid repetition. It should be noted that the results presented are already translated into millimeters using the method explained in the study [10]. Figure 2 shows the time it takes for a beam to finish the full deflection cycle, that is, the deflection from the rest position to the final position or the maximum deflection and from the final position back to the rest position.

During heating, the beam deflects from the rest position to the maximum deflection and the reverse during cooling. It is clearly seen from the figure that the beam's maximum deflection is reached in less than 10 s which is very quick. This quickness is suggested to be related to the wire diameter. The smaller the diameter, the faster the response of the wire. It is noted in

Figure 2. Time-deflection curve.

the figure that there is a flatness of the graph between 10 and 70 s. This flatness shows the beginning of the cooling cycle. It should be remembered that the driving force behind this graph is the NiTi SMA wire phase transition as discussed in Section 1. The martensite phase transforms to austenite phase between 0 and 10 s upon heating. The austenite phase is the dominant phase between 10 and 70 s, and then the nucleation of martensite starts to occur after 70 s. Martensite start occurs after 70 s and finishes after 140 s. The flatness behavior is seen after 140 s which depicts the domination of martensite phase. The number of data points between 0 and 10 s are few compared to the rest of the graph, and this is caused by the fact that the sampling rate was not easy to control.

Figure 3. SMA wire force-temperature graph.

Linear Shape Memory Alloy Thermomechanical Actuators

http://dx.doi.org/10.5772/intechopen.76292

63

Figure 4. Steel beam deflection-temperature graph.

The SMA wire force, which produced the maximum deflection of the steel beam, is shown in Figure 3. The maximum force produced by the current SMA wire (184-mm long) was found to be approximately 35.87517 N (~3.5 kg).

Figure 3 shows the deflection of the beam to the negative vertical (y) direction as the temperature increases and the reverse during cooling. It is noted that all the values on the y-axis of each figure are negative. This indicates that the direction of steel beam is to the negative ydirection. It is noted also that the curves (from Figures 2–4) are not smooth, and this is caused by the uncontrolled environmental conditions. The maximum deflection is taken with consideration of the sign of the value since it symbolizes the axis direction.

The deflection test results seem to be in agreement with the general behavior of shape memory alloy material. Therefore, these results will be used as the benchmark for simulation results and will be compared with FEA results in the following section.

Figure 3. SMA wire force-temperature graph.

the figure that there is a flatness of the graph between 10 and 70 s. This flatness shows the beginning of the cooling cycle. It should be remembered that the driving force behind this graph is the NiTi SMA wire phase transition as discussed in Section 1. The martensite phase transforms to austenite phase between 0 and 10 s upon heating. The austenite phase is the dominant phase between 10 and 70 s, and then the nucleation of martensite starts to occur after 70 s. Martensite start occurs after 70 s and finishes after 140 s. The flatness behavior is seen after 140 s which depicts the domination of martensite phase. The number of data points between 0 and 10 s are few compared to the rest of the graph, and this is caused by the fact

The SMA wire force, which produced the maximum deflection of the steel beam, is shown in Figure 3. The maximum force produced by the current SMA wire (184-mm long) was found to

Figure 3 shows the deflection of the beam to the negative vertical (y) direction as the temperature increases and the reverse during cooling. It is noted that all the values on the y-axis of each figure are negative. This indicates that the direction of steel beam is to the negative ydirection. It is noted also that the curves (from Figures 2–4) are not smooth, and this is caused by the uncontrolled environmental conditions. The maximum deflection is taken with consid-

The deflection test results seem to be in agreement with the general behavior of shape memory alloy material. Therefore, these results will be used as the benchmark for simulation results

eration of the sign of the value since it symbolizes the axis direction.

and will be compared with FEA results in the following section.

that the sampling rate was not easy to control.

be approximately 35.87517 N (~3.5 kg).

Figure 2. Time-deflection curve.

62 Shape-Memory Materials

Figure 4. Steel beam deflection-temperature graph.

## 5. Finite element analysis on a 2D beam setup

This section reflects the application of the proposed NiTi SMA model in predicting the response of the steel beam subjected to mechanical loading from NiTi SMA wire. Prior to the performance of the finite element analysis, an experiment was performed so as to find the simulation parameters like transformation temperature, the beam effective length and breadth, SMA wire effective length, and so on. To perform finite element analysis, a four-noded beam bar structure was constructed as shown in Figure 5. Two elements were steel beam elements and one bar element was NiTi SMA wire.

Element 1:

Element 2:

f ð Þ<sup>1</sup> <sup>¼</sup>

<sup>u</sup>ð Þ<sup>1</sup> <sup>¼</sup>

f ð Þ<sup>2</sup> <sup>¼</sup>

<sup>u</sup>ð Þ<sup>2</sup> <sup>¼</sup>

Figure 6. Plane bar elements in its local and global system.

f y1 mθR<sup>1</sup> f y2 mθR<sup>2</sup>

uy<sup>1</sup> θR<sup>1</sup> uy<sup>2</sup> θR<sup>2</sup>

f y2 mθR<sup>2</sup> f y3 mθR<sup>3</sup>

uy<sup>2</sup> θR<sup>2</sup> uy<sup>3</sup> θR<sup>3</sup>

(12)

65

(13)

Linear Shape Memory Alloy Thermomechanical Actuators

http://dx.doi.org/10.5772/intechopen.76292

Figure 5. Steel beam bar-SMA setup.

## 6. SMA model implementation

This section deals with the computer implementation of the finite element analysis. The local and the global plane beam bar element systems are being demonstrated schematically and are shown in Figure 6. The system has got three elements where each element has six degrees of freedom (three degrees of freedom per node). The axial degrees of freedom are ignored due to the nature of loading, hence the degrees of freedom per node are reduced from three to two, and therefore each element remains with four degrees of freedom (i.e. vertical displacement and rotation). The element node displacements and forces are given by Eqs. (12)–(14) as follows:

Element 1:

5. Finite element analysis on a 2D beam setup

and one bar element was NiTi SMA wire.

64 Shape-Memory Materials

6. SMA model implementation

Figure 5. Steel beam bar-SMA setup.

follows:

This section reflects the application of the proposed NiTi SMA model in predicting the response of the steel beam subjected to mechanical loading from NiTi SMA wire. Prior to the performance of the finite element analysis, an experiment was performed so as to find the simulation parameters like transformation temperature, the beam effective length and breadth, SMA wire effective length, and so on. To perform finite element analysis, a four-noded beam bar structure was constructed as shown in Figure 5. Two elements were steel beam elements

This section deals with the computer implementation of the finite element analysis. The local and the global plane beam bar element systems are being demonstrated schematically and are shown in Figure 6. The system has got three elements where each element has six degrees of freedom (three degrees of freedom per node). The axial degrees of freedom are ignored due to the nature of loading, hence the degrees of freedom per node are reduced from three to two, and therefore each element remains with four degrees of freedom (i.e. vertical displacement and rotation). The element node displacements and forces are given by Eqs. (12)–(14) as

$$\begin{aligned} f^{(1)} &= \begin{bmatrix} f\_{y1} \\ m\_{\theta \& 1} \\ f\_{y2} \\ m\_{\theta \& 2} \end{bmatrix} \\ u^{(1)} &= \begin{bmatrix} u\_{y1} \\ \theta\_{R1} \\ u\_{y2} \\ \theta\_{R2} \end{bmatrix} \end{aligned} \tag{12}$$

Element 2:

$$\begin{aligned} f^{(2)} &= \begin{bmatrix} f\_{y2} \\ m\_{\theta R2} \\ f\_{y3} \\ m\_{\theta R3} \end{bmatrix} \\ \underline{u}^{(2)} &= \begin{bmatrix} u\_{y2} \\ \theta\_{R2} \\ u\_{y3} \\ \theta\_{R3} \end{bmatrix} \end{aligned} \tag{13}$$

Figure 6. Plane bar elements in its local and global system.

Element 3:

$$\begin{aligned} \underline{f^{(3)}} &= \begin{bmatrix} f\_{x2} \\ f\_{y2} \\ f\_{4x} \\ f\_{4y} \end{bmatrix} \\ \underline{u^{(3)}} &= \begin{bmatrix} u\_{x2} \\ u\_{y2} \\ u\_{4x} \\ u\_{4x} \end{bmatrix} \end{aligned} \tag{14}$$

The force-temperature curves are shown in Figure 9. This graph shows the force variation which is effected by the temperature variation. The negative values indicate that the SMA wire was contracting. The maximum deflection (in Figure 8) was produced by a force of approximately 35.0 N (in Figure 9). The numerical results are in agreement with the experimental results with minor negligible difference. It can be seen from the figure that the numerical

Linear Shape Memory Alloy Thermomechanical Actuators

http://dx.doi.org/10.5772/intechopen.76292

67

prediction follows a similar trend with experiment.

Figure 7. Finite element program solution flow process.

For beam stiffness calculations, the only material properties required are the modulus of elasticity E, the second moment of area I and the length L of the beam. For the bar stiffness calculation, the only properties required are the cross-sectional area A, the modulus of elasticity E and the length L of the bar. These properties are taken to be constant throughout the bar and the beam. The solution procedure for our present problem is shown in Appendix A.

The schematic diagram for solution flow is shown in Figure 7. The solution diagram is a general solution flow to be used to solve one-sided temperature and phase coupling of any given 2-D geometry. In our case, we assume that phases are only affected by temperature and not by stress or pressure. The temperature affects the calculation of volume fraction through Eqs. (9) and (10). The linear averaged property (Young's modulus, E) is then calculated together with other parameters mentioned under phase transformation section.

The stiffness matrix of beam is formed using material properties of the beam and then that affects the formation of forces due to shape memory effect which is triggered by temperature variation. In our case, there are no external loads. This brings us to the calculation of the linear solution of Eq. (A8) from Appendix A. The process gets repeated until the maximum allowed temperature is reached.

Figure 7 summarizes the solution flow process of the developed simulation tool.

## 7. Simulation and experimental results

This section reflects the numerical results obtained from 1D finite element analysis. The material parameters used during FEA simulation are tabulated in Table 1. These parameters were derived from experiment using the procedure available in the study [11].

Figure 8 shows the deflection-time graph where we wanted to see if the numerical results would match the experimental results. Therefore, based on the results, it can be seen that the simulation curve resembles the experimental curve. Both curves show the maximum deflection of about 4.9 mm in less than 10 s. The two curves follow the same trend and they both do not exceed the maximum deflection of 5 mm.

Figure 7. Finite element program solution flow process.

Element 3:

66 Shape-Memory Materials

temperature is reached.

7. Simulation and experimental results

exceed the maximum deflection of 5 mm.

f ð Þ<sup>3</sup> <sup>¼</sup>

<sup>u</sup>ð Þ<sup>3</sup> <sup>¼</sup>

f x2 f y2 f 4x f 4y

> ux<sup>2</sup> uy<sup>2</sup> u4<sup>x</sup> u4<sup>x</sup>

(14)

For beam stiffness calculations, the only material properties required are the modulus of elasticity E, the second moment of area I and the length L of the beam. For the bar stiffness calculation, the only properties required are the cross-sectional area A, the modulus of elasticity E and the length L of the bar. These properties are taken to be constant throughout the bar and the beam. The solution procedure for our present problem is shown in Appendix A.

The schematic diagram for solution flow is shown in Figure 7. The solution diagram is a general solution flow to be used to solve one-sided temperature and phase coupling of any given 2-D geometry. In our case, we assume that phases are only affected by temperature and not by stress or pressure. The temperature affects the calculation of volume fraction through Eqs. (9) and (10). The linear averaged property (Young's modulus, E) is then calculated

The stiffness matrix of beam is formed using material properties of the beam and then that affects the formation of forces due to shape memory effect which is triggered by temperature variation. In our case, there are no external loads. This brings us to the calculation of the linear solution of Eq. (A8) from Appendix A. The process gets repeated until the maximum allowed

This section reflects the numerical results obtained from 1D finite element analysis. The material parameters used during FEA simulation are tabulated in Table 1. These parameters

Figure 8 shows the deflection-time graph where we wanted to see if the numerical results would match the experimental results. Therefore, based on the results, it can be seen that the simulation curve resembles the experimental curve. Both curves show the maximum deflection of about 4.9 mm in less than 10 s. The two curves follow the same trend and they both do not

together with other parameters mentioned under phase transformation section.

Figure 7 summarizes the solution flow process of the developed simulation tool.

were derived from experiment using the procedure available in the study [11].

> The force-temperature curves are shown in Figure 9. This graph shows the force variation which is effected by the temperature variation. The negative values indicate that the SMA wire was contracting. The maximum deflection (in Figure 8) was produced by a force of approximately 35.0 N (in Figure 9). The numerical results are in agreement with the experimental results with minor negligible difference. It can be seen from the figure that the numerical prediction follows a similar trend with experiment.


Table 1. Measured material parameters for 0.5-mm diameter NiTi SMA wire.

Figure 9. Force-temperature curves.

Figure 10. Experimental and numerical results for deflection-temperature curve.

Linear Shape Memory Alloy Thermomechanical Actuators

http://dx.doi.org/10.5772/intechopen.76292

69

Figure 8. Deflection-time curve.

The maximum deflection for a steel beam as a function of temperature is shown in Figure 10. This figure shows graphical comparison between the numerical and the experimental results. The maximum deflection obtained experimentally agrees to that obtained numerically. The minor difference between the experimental and the numerical results is seen during the cooling path, and this is suggested to be caused by the uncontrolled environmental conditions. It can be concluded that the developed mathematical equations can be used to predict the behavior of smart simple structures.

Figure 9. Force-temperature curves.

The maximum deflection for a steel beam as a function of temperature is shown in Figure 10. This figure shows graphical comparison between the numerical and the experimental results. The maximum deflection obtained experimentally agrees to that obtained numerically. The minor difference between the experimental and the numerical results is seen during the cooling path, and this is suggested to be caused by the uncontrolled environmental conditions. It can be concluded that the developed mathematical equations can be used to predict the

Property Value Units EM 16.8 GPa EA 31.8 GPa AM 0.6 <sup>o</sup>

AA 0.06 <sup>o</sup>

ξ<sup>M</sup> 0.5 — As 43 <sup>o</sup>

MF 18.3 <sup>o</sup>

Table 1. Measured material parameters for 0.5-mm diameter NiTi SMA wire.

ε<sup>L</sup> 0.0485 mm/mm ASMA 1.9635E7 m<sup>2</sup>

C<sup>1</sup>

C<sup>1</sup>

C

C

behavior of smart simple structures.

Figure 8. Deflection-time curve.

68 Shape-Memory Materials

Figure 10. Experimental and numerical results for deflection-temperature curve.

## 8. Conclusion

A finite element analysis based on the proposed SMA model was performed successfully. The finite element analysis was performed on the 1D setup which was oriented on the 2D space. The C++ code was developed in order to perform the 2D numerical analysis. The experiment was performed in order to obtain the parameters to input in the developed code and also to validate the numerical results. The maximum deflection obtained numerically matches that which was measured experimentally. It was verified through the results that the developed SMA model has the ability to capture all the temperature range and not only the intended range.

## A. Beam bar elements used to solve our system presented in the main text

The element stiffness matrix in global coordinates (X,Y) is explicitly given as follows: Element 1:

$$
\begin{bmatrix} K^{(1)} \\ \end{bmatrix} = \frac{EI}{L^3} \begin{bmatrix} 12 & 6L & -12 & 6L \\ 6L & 4L^2 & -6L & 2L^2 \\ -12 & -6L & 12 & -6L \\ 6L & 2L^2 & -6L & 4L^2 \\ \end{bmatrix} \begin{matrix} u\_1 \\ \theta\_1 \\ u\_2 \\ \theta\_2 \\ \end{matrix} \tag{A1}$$

The next step is the assemblage of the above stiffness matrix to get the global stiffness matrix.

EI

EI

<sup>L</sup><sup>3</sup> <sup>0</sup> � <sup>12</sup>EI

AE <sup>L</sup> � <sup>6</sup>EI L2

<sup>L</sup> � <sup>6</sup>EI

L þ

<sup>L</sup><sup>3</sup> � <sup>6</sup>EI L2

EI

0 0 0 0 0 0 00

<sup>L</sup><sup>2</sup> 0 0 00

<sup>L</sup> 0 0 00

EI

EI

EI

<sup>L</sup><sup>3</sup> � <sup>6</sup>EI

<sup>L</sup> 0 00 AE

EI

EI

EI

<sup>L</sup><sup>3</sup> � <sup>6</sup>EI

<sup>L</sup> 0 00 AE

<sup>L</sup><sup>2</sup> 0 0

<sup>L</sup> <sup>0</sup> AE

<sup>L</sup><sup>2</sup> 0 0

<sup>L</sup> 0 0

Lbar � �U2<sup>y</sup> (A7)

L

L

<sup>L</sup><sup>2</sup> 0 0

Linear Shape Memory Alloy Thermomechanical Actuators

http://dx.doi.org/10.5772/intechopen.76292

<sup>L</sup> <sup>0</sup> AE

<sup>L</sup><sup>2</sup> 0 0

<sup>L</sup> 0 0

L

(A4)

L

u1 θ1 u2 v2 u3 θ3 u4 v4

(A5)

(A6)

L3

EI

L2

<sup>L</sup><sup>2</sup> 0 0 00

<sup>L</sup> 0 0 00

L3

EI

L2

½ �¼ KG

The structural equation would be

EI L3

EI L2

EI L2

� <sup>12</sup>EI

F1<sup>x</sup> M<sup>1</sup> F2<sup>x</sup> F2<sup>y</sup> F3<sup>x</sup> M<sup>3</sup> F4<sup>x</sup> F4<sup>y</sup>

EI L3

EI L2

EI L2

� <sup>12</sup>EI

EI

EI

EI

0 0 � <sup>12</sup>EI

0 0 <sup>6</sup>EI

EI

EI

EI

0 0 � <sup>12</sup>EI

0 0 <sup>6</sup>EI

The boundary conditions for our system are as follows:

<sup>L</sup><sup>3</sup> � <sup>6</sup>EI L2

<sup>L</sup><sup>3</sup> � <sup>6</sup>EI L2

<sup>L</sup><sup>2</sup> � <sup>12</sup>EI

<sup>L</sup> � <sup>6</sup>EI L2

EI

<sup>L</sup> <sup>0</sup> <sup>8</sup>EI

L2

0 00 � AE

L3

EI

EI

<sup>L</sup><sup>3</sup> <sup>0</sup> � <sup>12</sup>EI

AE <sup>L</sup> � <sup>6</sup>EI L2

<sup>L</sup> � <sup>6</sup>EI

L þ

<sup>L</sup><sup>3</sup> � <sup>6</sup>EI L2

EI

0 0 0 0 0 0 00

Fx<sup>1</sup> ¼ M<sup>1</sup> ¼ Fx<sup>3</sup> ¼ M<sup>3</sup> ¼ Fx<sup>2</sup> ¼ Fx<sup>4</sup> ¼ Fy<sup>4</sup> ¼ 0

Lbeam þ AE

ux<sup>1</sup> ¼ θ<sup>1</sup> ¼ ux<sup>3</sup> ¼ θ<sup>3</sup> ¼ ux<sup>4</sup> ¼ uy<sup>4</sup> ¼ 0

FSMA <sup>¼</sup> <sup>8</sup>EI

<sup>L</sup><sup>2</sup> � <sup>12</sup>EI

<sup>L</sup> � <sup>6</sup>EI L2

EI

<sup>L</sup> <sup>0</sup> <sup>8</sup>EI

L2

0 00 � AE

Fy<sup>2</sup> ¼ FSMA

The structural equation reduces to the following equation:

L3

Element 2:

$$
\begin{bmatrix} K^{(1)} \\ \end{bmatrix} = \frac{EI}{L^3} \begin{bmatrix} 12 & 6L & -12 & 6L \\ 6L & 4L^2 & -6L & 2L^2 \\ -12 & -6L & 12 & -6L \\ 6L & 2L^2 & -6L & 4L^2 \\ \end{bmatrix} \begin{matrix} u\_2 \\ \theta\_2 \\ u\_3 \\ \theta\_3 \\ \end{matrix} \tag{A2}$$

Element 3:

$$
\begin{bmatrix} K^{(3)} \\ \end{bmatrix} = \begin{bmatrix} kc^2 & k\text{sc} & -kc^2 & -k\text{sc} \\ k\text{sc} & k\text{s}^2 & -k\text{sc} & -k\text{s}^2 \\ -kc^2 & -k\text{sc} & kc^2 & k\text{sc} \\ -k\text{sc} & -k\text{s}^2 & k\text{sc} & k\text{s}^2 \\ \end{bmatrix} = k \begin{bmatrix} c^2 & sc & -c^2 & -s c \\ sc & s^2 & -s c & -s^2 \\ -c^2 & -s c & c^2 & sc \\ -s c & -s^2 & sc & s^2 \\ \end{bmatrix} u\_{4x}
$$

$$\theta = 270^0; c = 0; \mathbf{s} = -1; \mathbf{cs} = 0\tag{A3}$$

$$
\begin{bmatrix} K^{(3)} \\ \end{bmatrix} = \frac{AE}{L} \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 1 \\ \end{bmatrix} \begin{matrix} \mu\_{23} \\ \nu\_{23} \\ \mu\_{43} \\ \end{matrix}
$$

The next step is the assemblage of the above stiffness matrix to get the global stiffness matrix.

$$[\mathbf{K}\_{G}] = \begin{bmatrix} \frac{12EI}{L^{3}} & \frac{6EI}{L^{2}} & -\frac{12EI}{L^{3}} & \frac{6EI}{L^{2}} & 0 & 0 & 0 & 0\\ \frac{6EI}{L^{2}} & \frac{4EI}{L} & -\frac{6EI}{L^{2}} & \frac{2EI}{L} & 0 & 0 & 0 & 0\\ -\frac{12EI}{L^{3}} & \frac{6EI}{L^{2}} & \frac{24EI}{L^{3}} & 0 & -\frac{12EI}{L^{3}} & \frac{6EI}{L^{2}} & 0 & 0\\ \frac{6EI}{L^{2}} & \frac{2EI}{L} & 0 & \frac{8EI}{L} + \frac{AE}{L} & -\frac{6EI}{L^{2}} & \frac{2EI}{L} & 0 & \frac{AE}{L}\\ 0 & 0 & -\frac{12EI}{L^{3}} & -\frac{6EI}{L^{2}} & \frac{12EI}{L^{3}} & -\frac{6EI}{L^{2}} & 0 & 0\\ 0 & 0 & \frac{6EI}{L^{2}} & \frac{2EI}{L} & -\frac{6EI}{L^{2}} & \frac{4EI}{L} & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & -\frac{AE}{L} & 0 & 0 & 0 & \frac{AE}{L} \end{bmatrix} \tag{A4}$$

The structural equation would be

8. Conclusion

Shape-Memory Materials

Element 1:

Element 2:

Element 3:

<sup>K</sup>ð Þ<sup>3</sup> h i 

<sup>θ</sup> <sup>¼</sup> 2700

<sup>K</sup>ð Þ<sup>3</sup> h i

 AE L

A finite element analysis based on the proposed SMA model was performed successfully. The finite element analysis was performed on the 1D setup which was oriented on the 2D space. The C++ code was developed in order to perform the 2D numerical analysis. The experiment was performed in order to obtain the parameters to input in the developed code and also to validate the numerical results. The maximum deflection obtained numerically matches that which was measured experimentally. It was verified through the results that the developed SMA model has

A. Beam bar elements used to solve our system presented in the main text

12 6L �12 6L <sup>L</sup> <sup>4</sup>L<sup>2</sup> �6<sup>L</sup> <sup>2</sup>L<sup>2</sup> �12 �6L 12 �6L <sup>L</sup> <sup>2</sup>L<sup>2</sup> �6<sup>L</sup> <sup>4</sup>L<sup>2</sup>

12 6L �12 6L <sup>L</sup> <sup>4</sup>L<sup>2</sup> �6<sup>L</sup> <sup>2</sup>L<sup>2</sup> �12 �6L 12 �6L <sup>L</sup> <sup>2</sup>L<sup>2</sup> �6<sup>L</sup> <sup>4</sup>L<sup>2</sup>

k

u2 θ2 u3 θ3

<sup>c</sup><sup>2</sup> sc �c<sup>2</sup> �sc sc s<sup>2</sup> �sc �s<sup>2</sup> �c<sup>2</sup> �sc c<sup>2</sup> sc �sc �s<sup>2</sup> sc s<sup>2</sup>

u2<sup>x</sup> u2<sup>y</sup> u4<sup>x</sup> u4<sup>y</sup>

u1 θ1 u2 θ2

(A1)

(A2)

(A3)

The element stiffness matrix in global coordinates (X,Y) is explicitly given as follows:

<sup>K</sup>ð Þ<sup>1</sup> h i

<sup>K</sup>ð Þ<sup>1</sup> h i

 EI L3

 EI L3

kc<sup>2</sup> ksc �kc<sup>2</sup> �ksc ksc ks<sup>2</sup> �ksc �ks<sup>2</sup> �kc<sup>2</sup> �ksc kc<sup>2</sup> ksc �ksc �ks<sup>2</sup> ksc ks<sup>2</sup>

; c ¼ 0; s ¼ �1; cs ¼ 0

u2<sup>x</sup> u2<sup>y</sup> u4<sup>x</sup> u4<sup>y</sup>

the ability to capture all the temperature range and not only the intended range.

$$
\begin{bmatrix} F\_{1x} \\ M\_1 \\ F\_{2x} \\ F\_{3y} \\ M\_3 \\ F\_{4y} \\ F\_{5y} \end{bmatrix} = \begin{bmatrix} \frac{12EI}{L^3} & \frac{6EI}{L^2} & -\frac{12EI}{L^3} & \frac{6EI}{L^2} & 0 & 0 & 0 & 0 \\ \frac{6EI}{L^2} & \frac{4EI}{L} & -\frac{6EI}{L^2} & \frac{2EI}{L} & 0 & 0 & 0 & 0 \\ -\frac{12EI}{L^3} & -\frac{6EI}{L^2} & \frac{24EI}{L^3} & 0 & -\frac{12EI}{L^3} & \frac{6EI}{L^2} & 0 & 0 \\ \frac{6EI}{L^2} & \frac{2EI}{L} & 0 & \frac{8EI}{L} + \frac{AE}{L} & -\frac{6EI}{L^2} & \frac{2EI}{L} & 0 & \frac{AE}{L} \\ 0 & 0 & -\frac{12EI}{L^3} & -\frac{6EI}{L^2} & \frac{12EI}{L^3} & -\frac{6EI}{L^2} & 0 & 0 \\ 0 & 0 & \frac{6EI}{L^2} & \frac{2EI}{L} & -\frac{6EI}{L^2} & \frac{4EI}{L} & 0 & 0 \\ 0 & 0 & \frac{6EI}{L^2} & \frac{2EI}{L} & -\frac{6EI}{L^2} & \frac{4EI}{L} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -\frac{AE}{L} & 0 & 0 & 0 & \frac{AE}{L} \end{bmatrix} \tag{A5}
$$

The boundary conditions for our system are as follows:

$$\begin{aligned} F\_{\ge 1} = M\_1 = F\_{\ge 3} = M\_3 = F\_{\ge 2} &= F\_{\ge 4} = F\_{y4} = 0\\ \mu\_{\ge 1} = \Theta\_1 = \mu\_{\ge 3} = \Theta\_3 = \mu\_{\ge 4} &= \mu\_{y4} = 0\\ F\_{y2} = F\_{SM4} \end{aligned} \tag{A6}$$

The structural equation reduces to the following equation:

$$F\_{SMA} = \left(\frac{8EI}{L\_{beam}} + \frac{AE}{L\_{bar}}\right) \mathcal{U}\_{2y} \tag{A7}$$

The deflection could be calculated as follows:

$$\frac{F\_{\text{SMA}}}{\left(\frac{8EI}{L\_{\text{low}}} + \frac{AE}{L\_{\text{low}}}\right)} = \mathcal{U}\_{2y} \tag{A8}$$

[8] Brinson LC. One-dimensional constitutive behaviour of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal

Linear Shape Memory Alloy Thermomechanical Actuators

http://dx.doi.org/10.5772/intechopen.76292

73

[9] Rajapakse RKND, Sun S. Simulation of pseudoelastic behaviour of SMA under cyclic

[10] Msomi V, Oliver GJ. Smart morphing based on shape memory alloy plate. Journal of

[11] Lagoudas DC, editor. Shape Memory Alloys: Modeling and Engineering Applications.

[12] Buravalla V, Khandelwal A. Evolution kinetics in shape memory alloys under arbitrary loading: Experiments and modeling. Journal of Mechanics and Materials. 2011;43:807-823

[13] Kamrani M, Kadkhodaei M. Investigation on local and global behaviours of pseudo elastic shape memory alloy wires in simple tensile test considering stress concentration of

[14] Zare F, Kadkhodaei M, Salafian I. Thermomechanical modelling of stress relaxation in shape memory alloy wires. Journal of Material Engineering and Performance. 2015;24(4):

[15] Shirani M, Kadkhodaei M. One dimensional constitutive model with transformation surfaces for phase transition in shape memory alloys considering the effect of loading

history. International Journal of Solids and Structures. 2016;81:117-129

grippers. Journal of Intelligence Material Systems and Structures. 2015;27:221-232

variable. Journal of Intelligent Materials and Structures. 1993;4(2):229-242

loading. Computational Materials Science. 2003;28:663-674

Engineering, Design and Technology. 2016;14(3):475-488

New York: Springer; 2008

1763-1770

This is the deflection that needs to be solved by the FEA. It should be noted that SMA force is the only variable in this equation, and also this SMA force is calculated inside the FEA code as follows:

$$F\_{\rm SMA} = \mathcal{E} A \varepsilon\_L \xi \tag{A9}$$

## Author details

Velaphi Msomi\* and Graeme Oliver

\*Address all correspondence to: msomiv@gmail.com

Cape Peninsula University of Technology, Bellville, South Africa

## References


[8] Brinson LC. One-dimensional constitutive behaviour of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable. Journal of Intelligent Materials and Structures. 1993;4(2):229-242

The deflection could be calculated as follows:

follows:

72 Shape-Memory Materials

Author details

References

1996;12(6):805-842

103-120

Velaphi Msomi\* and Graeme Oliver

\*Address all correspondence to: msomiv@gmail.com

Cape Peninsula University of Technology, Bellville, South Africa

FSMA 8EI Lbeam <sup>þ</sup> AE Lbar

This is the deflection that needs to be solved by the FEA. It should be noted that SMA force is the only variable in this equation, and also this SMA force is calculated inside the FEA code as

[1] Paiva A, Savi MA. An overview of constitutive models for shape memory alloys. Hindawi

[2] Tanaka K. A thermomechanical sketch of shape memory effect: One-dimensional tensile

[3] Tanaka K, Nagaki S. Thermomechanical description of materials with internal variables in

[4] Boyd JG, Lagoudas DC. A thermodynamic constitutive model for the shape memory materials. Part I: The monolithic shape memory alloys. International Journal of Plasticity.

[5] Liang C, Rogers CA. One-dimensional thermomechanical constitutive relations for shape memory materials. Journal of Intelligent Material Systems and Structures. 1990;1:207-234

[6] Anders WS, Rogers CA, Fuller CR. Vibration and low-frequency acoustic analysis of piecewise-activated adaptive composite panels. Journal of Composite Materials. 1992;26:

[7] Rogers CA, Liang C, Fuller CR. Modeling of shape memory alloy hybrid composites for structural acoustic control. Journal of Acoustic Society of America. 1991;89(1):210-220

Publishing Corporation (Mathematical Problems in Engineering). 2006;1:1-30

behavior. Materials Science Research International. 1985;18:251

the process of phase transitions. Ingenieur- Archive. 1982;51:287-299

<sup>¼</sup> <sup>U</sup>2<sup>y</sup> (A8)

FSMA ¼ EAεLξ (A9)


**Chapter 5**

Provisional chapter

**Experiments and Models of Thermo-Induced Shape**

DOI: 10.5772/intechopen.78012

Recent advances in experiments and models of thermo-induced shape memory polymers (TSMPs) were reviewed. Some important visco-elastic and visco-plastic features, such as rate-dependent and temperature-dependent stress-strain curves and nonuniform temperature distribution were experimentally investigated, and the interaction between the mechanical deformation and the internal heat generation was discussed. The influences of loading rate and peak strain on the shape memory effect (SME) and shape memory degeneration of TSMPs were revealed under monotonic and cyclic thermo-mechanical loadings, respectively. Based on experimental observations, the capability of recent developed visco-elastic and visco-plastic models for predicting the SME was evaluated, and the thermo-mechanically coupled models were used to reasonably predict the thermo-

Keywords: shape memory polymers, thermo-mechanical coupling, constitutive models,

Thermo-induced shape memory polymers (TSMPs) are one of most widely applicable shape memory polymers (SMPs) at present, which exhibit the shape memory effect (SME) by changing the ambient temperature. TSMPs are different from the traditional polymers; some of their important features related to the SME were summarized by Lendlein et al. [1] and Hager et al. [2] as follows: (1) a phase presents the rubber-like state in a wide temperature range above the glassy transition temperature (Tg) and has a stable strength to deform; (2) a

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Experiments and Models of Thermo-Induced Shape

**Memory Polymers**

Memory Polymers

Zebin Zhang

Zebin Zhang

Abstract

1. Introduction

Qianhua Kan, Jian Li, Guozheng Kang and

Qianhua Kan, Jian Li, Guozheng Kang and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78012

mechanical responses of TSMPs.

glassy transition, relaxation

#### **Experiments and Models of Thermo-Induced Shape Memory Polymers** Experiments and Models of Thermo-Induced Shape Memory Polymers

DOI: 10.5772/intechopen.78012

Qianhua Kan, Jian Li, Guozheng Kang and Zebin Zhang Qianhua Kan, Jian Li, Guozheng Kang and Zebin Zhang

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78012

#### Abstract

Recent advances in experiments and models of thermo-induced shape memory polymers (TSMPs) were reviewed. Some important visco-elastic and visco-plastic features, such as rate-dependent and temperature-dependent stress-strain curves and nonuniform temperature distribution were experimentally investigated, and the interaction between the mechanical deformation and the internal heat generation was discussed. The influences of loading rate and peak strain on the shape memory effect (SME) and shape memory degeneration of TSMPs were revealed under monotonic and cyclic thermo-mechanical loadings, respectively. Based on experimental observations, the capability of recent developed visco-elastic and visco-plastic models for predicting the SME was evaluated, and the thermo-mechanically coupled models were used to reasonably predict the thermomechanical responses of TSMPs.

Keywords: shape memory polymers, thermo-mechanical coupling, constitutive models, glassy transition, relaxation

## 1. Introduction

Thermo-induced shape memory polymers (TSMPs) are one of most widely applicable shape memory polymers (SMPs) at present, which exhibit the shape memory effect (SME) by changing the ambient temperature. TSMPs are different from the traditional polymers; some of their important features related to the SME were summarized by Lendlein et al. [1] and Hager et al. [2] as follows: (1) a phase presents the rubber-like state in a wide temperature range above the glassy transition temperature (Tg) and has a stable strength to deform; (2) a

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

2. Experiment observations

loading rates, as shown in Figure 2.

beyond the glassy transition temperature Tg.

2.2. Thermo-mechanical coupling behaviors

temperature changes induced by the internal heat generation.

The mechanical properties of TSMPs are strongly sensitive to the ambient temperature and the loading rate and can be obtained from tensile experiments at different temperatures and

Experiments and Models of Thermo-Induced Shape Memory Polymers

http://dx.doi.org/10.5772/intechopen.78012

77

It is found from Figure 2 that the high-stress responses at low temperature is a typical feature of amorphous polymers, and the low stress responses at high temperature is a typical feature of visco-elastic polymer. The yield peak gradually disappears when the temperature goes

The thermo-mechanical properties can be obtained from the dynamic mechanical analysis (DMA) [7]. As shown in Figure 3, the storage and loss moduli obtained from DMA are found as functions of temperature. The glassy transition temperature, where the ratio of loss modulus and storage modulus (tan δ) dramatically changes, can be obtained from the DMA results, and the glassy transition temperature increases with the frequency [8]. In addition, the glassy transition temperature can be also obtained from the differential scanning calorimeter (DSC)

The thermo-mechanical coupling behaviors are divided into two types here, one is that the mechanical behavior changes with the ambient temperature, that is, SME; the other is the

Figure 2. Stress-strain curves of monotonic tension at (a) different temperatures and (b) loading rates.

2.1. Mechanical performances

test [9].

Figure 1. The molecular mechanism of the SME of TSMPs [3].

phase presents the glass-like state in a wide temperature range below T<sup>g</sup> and has a stable strength to ensure that the internal stress is not be released in storage; (3) The two separable phases are the structural basis of SME and the suitable ratio between the two phases should be existent. The molecular mechanism of TSMPs was presented by Behl et al. [3], as shown in Figure 1. There are three parts in TSMPs, including the netpoint, the relaxed switching segment, the elongated and fixed switching segment (i.e., the transition phase, it can transform between the netpoint and the relaxed switching segment with the change of temperature).

The popular topics focus on the fabrications, the analysis of mechanisms and applications of TSMPs [3–5]. The constitutive models describing the glassy transition mechanism of TSMPs are summarized and they can be divided into two types according to different deformation mechanisms, including the thermo-visco-elastic rheology model and the meso-mechanical model [6]. The thermo-visco-elastic model can describe the mobility of chain segments and relaxation with temperature by introducing the relaxation time and the temperaturedependent modulus. The meso-mechanical model adopted a mixture rule of rubber and glassy phases by the volume fractions of frozen and active phases. For considering the interaction between the internal heat generation and mechanical deformation, the thermomechanically coupled models were developed by introducing different dissipation mechanisms.

In this chapter, recent advances in experiments and models of TSMPs are reviewed. According to experimental observations, some deformation mechanisms and features of TSMPs are summarized. The capability of two types of models in predicting the mechanical responses and the SME of TSMPs are evaluated, and some interesting issues and further developments of TSMPs were discussed in the end.

## 2. Experiment observations

## 2.1. Mechanical performances

phase presents the glass-like state in a wide temperature range below T<sup>g</sup> and has a stable strength to ensure that the internal stress is not be released in storage; (3) The two separable phases are the structural basis of SME and the suitable ratio between the two phases should be existent. The molecular mechanism of TSMPs was presented by Behl et al. [3], as shown in Figure 1. There are three parts in TSMPs, including the netpoint, the relaxed switching segment, the elongated and fixed switching segment (i.e., the transition phase, it can transform between the netpoint and the relaxed switching segment with the change of

The popular topics focus on the fabrications, the analysis of mechanisms and applications of TSMPs [3–5]. The constitutive models describing the glassy transition mechanism of TSMPs are summarized and they can be divided into two types according to different deformation mechanisms, including the thermo-visco-elastic rheology model and the meso-mechanical model [6]. The thermo-visco-elastic model can describe the mobility of chain segments and relaxation with temperature by introducing the relaxation time and the temperaturedependent modulus. The meso-mechanical model adopted a mixture rule of rubber and glassy phases by the volume fractions of frozen and active phases. For considering the interaction between the internal heat generation and mechanical deformation, the thermomechanically coupled models were developed by introducing different dissipation mecha-

In this chapter, recent advances in experiments and models of TSMPs are reviewed. According to experimental observations, some deformation mechanisms and features of TSMPs are summarized. The capability of two types of models in predicting the mechanical responses and the SME of TSMPs are evaluated, and some interesting issues and further developments of TSMPs

temperature).

76 Shape-Memory Materials

Figure 1. The molecular mechanism of the SME of TSMPs [3].

nisms.

were discussed in the end.

The mechanical properties of TSMPs are strongly sensitive to the ambient temperature and the loading rate and can be obtained from tensile experiments at different temperatures and loading rates, as shown in Figure 2.

It is found from Figure 2 that the high-stress responses at low temperature is a typical feature of amorphous polymers, and the low stress responses at high temperature is a typical feature of visco-elastic polymer. The yield peak gradually disappears when the temperature goes beyond the glassy transition temperature Tg.

The thermo-mechanical properties can be obtained from the dynamic mechanical analysis (DMA) [7]. As shown in Figure 3, the storage and loss moduli obtained from DMA are found as functions of temperature. The glassy transition temperature, where the ratio of loss modulus and storage modulus (tan δ) dramatically changes, can be obtained from the DMA results, and the glassy transition temperature increases with the frequency [8]. In addition, the glassy transition temperature can be also obtained from the differential scanning calorimeter (DSC) test [9].

#### 2.2. Thermo-mechanical coupling behaviors

The thermo-mechanical coupling behaviors are divided into two types here, one is that the mechanical behavior changes with the ambient temperature, that is, SME; the other is the temperature changes induced by the internal heat generation.

Figure 2. Stress-strain curves of monotonic tension at (a) different temperatures and (b) loading rates.

The SME process can be divided into stress-controlled (stress-free recovery) and straincontrolled (strain-constraint recovery) modes during strain recovery by heating, respectively. Two parameters are usually used to character the SME, including the shape fixity ratio Rf and

� 100 (1)

http://dx.doi.org/10.5772/intechopen.78012

79

Experiments and Models of Thermo-Induced Shape Memory Polymers

� 100 (2)

Rf <sup>¼</sup> <sup>ε</sup><sup>u</sup> εm

<sup>R</sup><sup>r</sup> <sup>¼</sup> <sup>ε</sup><sup>m</sup> � <sup>ε</sup><sup>r</sup> εm

where εm, ε<sup>u</sup> and ε<sup>r</sup> denote the peak strain, fixed strain and residual strain, respectively.

Besides, the recoverable glassy transition temperature in the stress-free recovery, the maximum recovery stress in the constraint recovery and the recoverable temperature at the maximum

The experimental results of TSMPs sheet (MM4520) at different strain rates and peak strains

It is found from Figure 5 that the maximum stress at the cooling stage decreases with the increase of loading rate, and the shape recovery ratio of TSMPs in the stress-free recovery decreases with the increase of peak strain and the decrease of strain rate, which is similar with shape memory experiments of TSMPs sheet (MS4510) [14]. It is the reason that the viscosity increases with the increase of strain rate and the damage in chain segments increases with the increase of peak strain. The correlation between the loading rate and the shape recovery ratio can be explained, as the relaxation of the stored elastic energy is easier at low loading rate than at high loading rate. However, the SME in the stress-free recovery is independent on the peak strain; the recovery maximum stress increases with the increase of peak strain for the aliphatic

In the molecular level, a prior orientation of switching chain segments of thermoplastic TSMPs improves with the increase of macroscopic deformation; once these chain segments return to the random coil-like conformation, the maximum recovery stress increases in the strainconstraint recovery. However, the peak strain has almost no influence on the SME for the

Figure 5. Stress-strain-temperature curves at different (a) strain rates, (b) peak strains, and (c) shape recovery ratio versus

the shape recovery ratio R<sup>r</sup> [10, 11] as shown in Eqs. (1) and (2).

recovery stress are also used to quantify the SME [10–13].

are shown in Figure 5.

polyether urethane [13].

peak strain at different strain rates.

Figure 3. The curves of storage modulus, loss modulus, and tanδ versus temperature.

Figure 4. The illustration of SME of TSMPs.

#### 2.2.1. Shape memory effect

As shown in Figure 4, a typical SME process includes four stages, that is, Step1: deforming at high temperature above Tg; Step2: cooling to the storage temperature (room temperature in general); Step3: unloading at the storage temperature and the shape is fixed; Step4: heating to the recoverable temperature above Tg, the deformed shape returns to the initial undeformed shape.

The SME process can be divided into stress-controlled (stress-free recovery) and straincontrolled (strain-constraint recovery) modes during strain recovery by heating, respectively. Two parameters are usually used to character the SME, including the shape fixity ratio Rf and the shape recovery ratio R<sup>r</sup> [10, 11] as shown in Eqs. (1) and (2).

$$R\_f = \frac{\varepsilon\_u}{\varepsilon\_m} \times 100\tag{1}$$

$$R\_{\rm r} = \frac{\varepsilon\_{\rm m} - \varepsilon\_{\rm r}}{\varepsilon\_{\rm m}} \times 100 \tag{2}$$

where εm, ε<sup>u</sup> and ε<sup>r</sup> denote the peak strain, fixed strain and residual strain, respectively.

Besides, the recoverable glassy transition temperature in the stress-free recovery, the maximum recovery stress in the constraint recovery and the recoverable temperature at the maximum recovery stress are also used to quantify the SME [10–13].

The experimental results of TSMPs sheet (MM4520) at different strain rates and peak strains are shown in Figure 5.

It is found from Figure 5 that the maximum stress at the cooling stage decreases with the increase of loading rate, and the shape recovery ratio of TSMPs in the stress-free recovery decreases with the increase of peak strain and the decrease of strain rate, which is similar with shape memory experiments of TSMPs sheet (MS4510) [14]. It is the reason that the viscosity increases with the increase of strain rate and the damage in chain segments increases with the increase of peak strain. The correlation between the loading rate and the shape recovery ratio can be explained, as the relaxation of the stored elastic energy is easier at low loading rate than at high loading rate. However, the SME in the stress-free recovery is independent on the peak strain; the recovery maximum stress increases with the increase of peak strain for the aliphatic polyether urethane [13].

In the molecular level, a prior orientation of switching chain segments of thermoplastic TSMPs improves with the increase of macroscopic deformation; once these chain segments return to the random coil-like conformation, the maximum recovery stress increases in the strainconstraint recovery. However, the peak strain has almost no influence on the SME for the

2.2.1. Shape memory effect

78 Shape-Memory Materials

Figure 4. The illustration of SME of TSMPs.

Figure 3. The curves of storage modulus, loss modulus, and tanδ versus temperature.

shape.

As shown in Figure 4, a typical SME process includes four stages, that is, Step1: deforming at high temperature above Tg; Step2: cooling to the storage temperature (room temperature in general); Step3: unloading at the storage temperature and the shape is fixed; Step4: heating to the recoverable temperature above Tg, the deformed shape returns to the initial undeformed

Figure 5. Stress-strain-temperature curves at different (a) strain rates, (b) peak strains, and (c) shape recovery ratio versus peak strain at different strain rates.

thermoset TSMPs [12, 15] since the thermoset TSMPs have a more stable molecular structure than the thermoplastic TSMPs.

Hu et al. [14] found that TSMPs film (MS4510) exhibits an excellent SME at the temperature range from T<sup>g</sup> to T<sup>g</sup> + 25C, and the shape recovery ratio decreases beyond the temperature range. To obtain better SME in practical applications, the TSMPs film should be cooled to its frozen state as soon as possible after being deformed at high temperature. Cui and Lendlein [13] found the switching temperature of shape recovery in the stress-free recovery, the maximum recovery stress and the corresponding temperature in the strain-constraint recovery increase with the increase of deformation temperature. The start temperature of shape recovery can be controlled by adjusting the cooling temperature during unloading [16].

Besides, many factors can remarkably affect the shape recovery ratio, for example, the shape recovery ratio decreases with the increase of holding time after deformation since the increase of holding time causes a large relaxation of the stored elastic energy [17, 18]. The shape recovery ratio increases with the increase of finish recovery temperature since the mobility of chain segments is more active at high temperature [14, 18]. If the recovery temperature is higher than the deformation temperature, the inactive chain segments during the deforming stage can be activated to increase their mobility. The shape recovery ratio increases with the decrease of heating rate since the heat conduction of TSMPs requires enough time. If the holding time increases after approaching the finish recovery temperature, the effect of heating rate on the shape recovery ratio can be eliminated [15].

According to the experiment results, the mobility of chain segments, visco-elasticity, stress relaxation and structural relaxation of TSMPs also have influences on the SME. These influential factors change with temperature and can be utilized to optimize the SME.

## 2.2.2. Internal heat generation induced by deformation

TSMPs are sensitive to the temperatures, including the temperature caused by the internal heat generation and ambient temperature. According to the thermo-mechanically coupled experiments [8, 19, 20], an infrared camera is used to measure the surface temperature of TSMPs for indicating the interaction between mechanical deformation and temperature. It is concluded that TSMPs are very sensitive to the temperature and loading rate, and the temperature localization is related to the strain localization, as shown in Figures 6–8. The temperature firstly decreases during the elastic deformation stage and then increases during visco-plastic deformation stage in tension, which implies that the internal heat generation is contributed by two parts, that is, the decreased temperature due to the thermo-elastic effect and the increased temperature due to the visco-plastic dissipation. It is noted from Figure 7 that the temperature variation increases with the increase of loading rate and it can be explained as with the increase of loading rate in tension, the resistance of the slipping of chain segments increases, which results in a larger dissipation caused by the friction of disentanglement of chain segments.

increase of number of cycles. It is the reason that the decreased stress at peak strain due to the stress relaxation and the accumulated residual strain after unloading result in a narrower and narrower hysteresis loop, that is, decreased visco-plastic dissipation with the increase of

Figure 6. (a) Curves of stress-strain and strain-temperature variation; and (b) temperature field distribution.

Experiments and Models of Thermo-Induced Shape Memory Polymers

http://dx.doi.org/10.5772/intechopen.78012

81

When the TSMPs are subjected to thermo-mechanical cyclic loadings (i.e., repeated shape memory cycles), the shape memory degradation can be characterized by the strain recovery

rate Rrate [11, 21] and strain recovery ratio Rratio [22], respectively, as below:

Figure 7. Curves of temperature versus position corresponding to Figure 6(b).

number of cycles.

2.3. Shape memory degradation

The stress-strain curves and temperature variations of TSMPs subjected to loading-unloading mechanical cycles were obtained by Pieczyska et al. [20], as shown in Figure 9. It is found that the residual strain accumulates and the amplitude of temperature variation decreases with the Experiments and Models of Thermo-Induced Shape Memory Polymers http://dx.doi.org/10.5772/intechopen.78012 81

Figure 6. (a) Curves of stress-strain and strain-temperature variation; and (b) temperature field distribution.

Figure 7. Curves of temperature versus position corresponding to Figure 6(b).

increase of number of cycles. It is the reason that the decreased stress at peak strain due to the stress relaxation and the accumulated residual strain after unloading result in a narrower and narrower hysteresis loop, that is, decreased visco-plastic dissipation with the increase of number of cycles.

#### 2.3. Shape memory degradation

thermoset TSMPs [12, 15] since the thermoset TSMPs have a more stable molecular structure

Hu et al. [14] found that TSMPs film (MS4510) exhibits an excellent SME at the temperature range from T<sup>g</sup> to T<sup>g</sup> + 25C, and the shape recovery ratio decreases beyond the temperature range. To obtain better SME in practical applications, the TSMPs film should be cooled to its frozen state as soon as possible after being deformed at high temperature. Cui and Lendlein [13] found the switching temperature of shape recovery in the stress-free recovery, the maximum recovery stress and the corresponding temperature in the strain-constraint recovery increase with the increase of deformation temperature. The start temperature of shape recov-

Besides, many factors can remarkably affect the shape recovery ratio, for example, the shape recovery ratio decreases with the increase of holding time after deformation since the increase of holding time causes a large relaxation of the stored elastic energy [17, 18]. The shape recovery ratio increases with the increase of finish recovery temperature since the mobility of chain segments is more active at high temperature [14, 18]. If the recovery temperature is higher than the deformation temperature, the inactive chain segments during the deforming stage can be activated to increase their mobility. The shape recovery ratio increases with the decrease of heating rate since the heat conduction of TSMPs requires enough time. If the holding time increases after approaching the finish recovery temperature, the effect of heating

According to the experiment results, the mobility of chain segments, visco-elasticity, stress relaxation and structural relaxation of TSMPs also have influences on the SME. These influen-

TSMPs are sensitive to the temperatures, including the temperature caused by the internal heat generation and ambient temperature. According to the thermo-mechanically coupled experiments [8, 19, 20], an infrared camera is used to measure the surface temperature of TSMPs for indicating the interaction between mechanical deformation and temperature. It is concluded that TSMPs are very sensitive to the temperature and loading rate, and the temperature localization is related to the strain localization, as shown in Figures 6–8. The temperature firstly decreases during the elastic deformation stage and then increases during visco-plastic deformation stage in tension, which implies that the internal heat generation is contributed by two parts, that is, the decreased temperature due to the thermo-elastic effect and the increased temperature due to the visco-plastic dissipation. It is noted from Figure 7 that the temperature variation increases with the increase of loading rate and it can be explained as with the increase of loading rate in tension, the resistance of the slipping of chain segments increases, which results in a larger dissipation caused by the friction of disentanglement of chain segments.

The stress-strain curves and temperature variations of TSMPs subjected to loading-unloading mechanical cycles were obtained by Pieczyska et al. [20], as shown in Figure 9. It is found that the residual strain accumulates and the amplitude of temperature variation decreases with the

tial factors change with temperature and can be utilized to optimize the SME.

ery can be controlled by adjusting the cooling temperature during unloading [16].

rate on the shape recovery ratio can be eliminated [15].

2.2.2. Internal heat generation induced by deformation

than the thermoplastic TSMPs.

80 Shape-Memory Materials

When the TSMPs are subjected to thermo-mechanical cyclic loadings (i.e., repeated shape memory cycles), the shape memory degradation can be characterized by the strain recovery rate Rrate [11, 21] and strain recovery ratio Rratio [22], respectively, as below:

Figure 8. (a) Stress-strain curves; (b) curves of average temperature variation versus strain; and (c) curves of maximum temperature variation versus strain.

Figure 9. Stress and temperature change of TSMPs subjected to loading-unloading cycles versus (a) true strain and (b) time [20].

$$R\_{\text{rate}}(\text{N}) = \frac{\varepsilon\_{\text{u}}(\text{N}) - \varepsilon\_{r}(\text{N})}{\varepsilon\_{\text{u}}(\text{N}) - \varepsilon\_{r}(\text{N-1})} \times 100 \tag{3}$$

$$R\_{\text{ratio}}(\text{N}) = \frac{\varepsilon\_m - \varepsilon\_r(\text{N})}{\varepsilon\_m} \times 100\tag{4}$$

recovery ratio of TSMPs can be improved by undergoing previous mechanical cycles since the mechanical training can eliminate the heterogeneous structure of chain segments [24]. How-

Conventional experimental methods limited within uniaxial tension or compression were discussed in Sections 2.1–2.3. Recently, many advanced experimental methods and complex loading modes were developed to investigate the SME of TSMPs. For example, the nanoindentation technology was used to examine the SME of TSMPs, and the indentation can be recovered by heating the sample to above the glass transition temperature [26]; this research

ever, the previous mechanical cycles have almost no influence on strain recovery rate.

Figure 11. The influences of previous mechanical cycles on the strain recovery rate and strain recovery ratio [25].

Figure 10. Curves of (a) the strain recovery rate [11] and (b) the strain recovery ratio [22] with number of cycles.

Experiments and Models of Thermo-Induced Shape Memory Polymers

http://dx.doi.org/10.5772/intechopen.78012

83

provides a foundation to explore the nano-mechanical behavior of TSMPs.

2.4. Novel experimental observations on SME

where ε<sup>m</sup> denotes the peak strain during loading, εuð Þ N and εrð Þ N denote the fixed strain and residual strain after unloading in the N-th cycle, respectively.

The experimental results subjected to shape memory cycles are shown in Figure 10 [11, 22]. It is found that the strain recovery rate gradually increases with the decrease of peak strain and the increase of number of cycles and rapidly approaches 100% after several cycles. However, the recovery strain ratio depends on the peak strain, for example, it increases with the increase of peak strain; however, it decreases when the peak strain is up to 150%.

The shape memory degeneration also depends on the deformable temperature, recovery temperature and mechanical training [22–25]. For example, as shown in Figure 11, the strain

Figure 10. Curves of (a) the strain recovery rate [11] and (b) the strain recovery ratio [22] with number of cycles.

Figure 11. The influences of previous mechanical cycles on the strain recovery rate and strain recovery ratio [25].

recovery ratio of TSMPs can be improved by undergoing previous mechanical cycles since the mechanical training can eliminate the heterogeneous structure of chain segments [24]. However, the previous mechanical cycles have almost no influence on strain recovery rate.

#### 2.4. Novel experimental observations on SME

<sup>R</sup>rateð Þ¼ <sup>N</sup> <sup>ε</sup>uð Þ� <sup>N</sup> <sup>ε</sup>rð Þ <sup>N</sup>

<sup>R</sup>ratioð Þ¼ <sup>N</sup> <sup>ε</sup><sup>m</sup> � <sup>ε</sup>rð Þ <sup>N</sup>

residual strain after unloading in the N-th cycle, respectively.

time [20].

temperature variation versus strain.

82 Shape-Memory Materials

of peak strain; however, it decreases when the peak strain is up to 150%.

εuð Þ� N εrð Þ N-1

Figure 9. Stress and temperature change of TSMPs subjected to loading-unloading cycles versus (a) true strain and (b)

Figure 8. (a) Stress-strain curves; (b) curves of average temperature variation versus strain; and (c) curves of maximum

εm

where ε<sup>m</sup> denotes the peak strain during loading, εuð Þ N and εrð Þ N denote the fixed strain and

The experimental results subjected to shape memory cycles are shown in Figure 10 [11, 22]. It is found that the strain recovery rate gradually increases with the decrease of peak strain and the increase of number of cycles and rapidly approaches 100% after several cycles. However, the recovery strain ratio depends on the peak strain, for example, it increases with the increase

The shape memory degeneration also depends on the deformable temperature, recovery temperature and mechanical training [22–25]. For example, as shown in Figure 11, the strain

� 100 (3)

� 100 (4)

Conventional experimental methods limited within uniaxial tension or compression were discussed in Sections 2.1–2.3. Recently, many advanced experimental methods and complex loading modes were developed to investigate the SME of TSMPs. For example, the nanoindentation technology was used to examine the SME of TSMPs, and the indentation can be recovered by heating the sample to above the glass transition temperature [26]; this research provides a foundation to explore the nano-mechanical behavior of TSMPs.

The shear deformation and its recovery behavior were investigated through a double lap joint arrangement at below and above T<sup>g</sup> [27]. Torsional shape memory tests were carried out to characterize the SME, and a torsional device with a CCD camera was used to quantify the parameters of the SME [28]. A series of tension, compression, bending and twisting experiments of TSMPs were performed to indicate the SME; it is shown that the heating rate has an obvious influence on the start temperature of shape recovery [29].

These experimental findings provide an experimental guidance for future applications, including aerospace, automotive, robotics, and smart actuator, and so on. Some novel experiments and protocols are expected to be designed for characterizing the SME of smart structures in future.

## 3. Constitutive models

Constitutive models of TSMPs, including shape memory model describing the SME and the thermo-mechanically coupled model describing the internal heat generation caused by mechanical deformation, are commented on in this section.

To describe the nonlinear behaviors of TSMPs, a one-dimensional nonlinear visco-elastic model was extended from a linear visco-elastic version [30]. However, the extended model provides an overestimation of the responded stress at large strain, and thus the linear model was further modified to reasonably simulate the SME of TSMPs at large strain by introducing new nonlinear evolution equations with stress threshold values into the cooling modulus and

It is noted that, even though the mechanical responses at large strain were simulated, the abovementioned models were established at small deformation. Therefore, Diani et al. [32] developed a thermo-mechanical model of TSMPs at finite deformation based on the three element standard linear visco-elastic model [21]. The total deformation gradient is decomposed into elastic and viscous parts. The total Cauchy stress includes the stresses caused by the

Nguyen et al. [33] developed a thermo-visco-elastic model to describe the time-dependent and temperature-dependent deformations of TSMPs by incorporating structural relaxation and stress relaxations. The model can reproduce the strain-temperature response, rate-dependent stress-strain response and some important features of temperature dependent shape memory responses. In the model, a fictive temperature Tf is used to describe the structural relaxation behavior and the structural relaxation time is obtained from the WLF equation, as shown in Eq. (6). The stress relaxation adopts the form of visco-elasticity in the glass transition region and rubbery state, and the modified WLF equation is introduced into the Eyring equation to obtain a modified visco-plastic flow rule for describing the visco-plastic deformation, includ-

log e

2 4

C<sup>2</sup> T � Tf

0 @

� � <sup>þ</sup> T Tf � <sup>T</sup>ref

� �

T C<sup>2</sup> <sup>þ</sup> Tf � <sup>T</sup>ref

C<sup>2</sup> T � Tf

g

� � <sup>þ</sup> T Tf � <sup>T</sup>ref

Experiments and Models of Thermo-Induced Shape Memory Polymers

http://dx.doi.org/10.5772/intechopen.78012

85

� �

1 A

3

T C<sup>2</sup> <sup>þ</sup> Tf � <sup>T</sup>ref

g � �

g � �

1 A

3

<sup>s</sup>neq k k ffiffiffi 2 <sup>p</sup> sy !

5 (6)

(7)

g

<sup>5</sup>sinh Qs T

irrecoverable strain [31].

Figure 12. Four-element model.

entropy change and internal energy change, respectively.

ing the glassy state and rubbery state, see Eq. (7).

T Qs exp

neq � � � � <sup>¼</sup> <sup>τ</sup>Rg exp � <sup>C</sup><sup>1</sup>

2 4

C1 log e 0 @

τ<sup>R</sup> T; Tf δ

<sup>γ</sup>\_ <sup>v</sup> <sup>¼</sup> sy ffiffiffi 2 <sup>p</sup> <sup>η</sup>ref sg

## 3.1. Shape memory model

Based on the different deformation mechanisms, different models were constructed to describe the SME of TSMPs, including the rheology model considering the mobility and relaxation and the meso-mechanical model considering the phase transition between the frozen and active phases.

## 3.1.1. Rheology model

The mobility of chain segments is a classical mechanism to describe the SME, which remarkably depends on ambient temperature. Tobushi et al. [21] think that the shape of TSMPs can be fixed due to the decreased mobility of chain segments with the decrease of temperature, and the shape can be recovered due to the increased mobility of chain segments with the increase of temperature. Therefore, a rheological model was proposed by introducing a slip element into a three-element standard linear visco-elastic model, as shown in Figure 12, and the mobility of chain segments can be expressed as the exponential functions between material parameters and temperature, as shown in Eq. (5).

$$\mathbf{x}(T) = \begin{cases} \mathbf{x}(T\_l) & (T \le T\_l) \\\ x\_\mathbf{g} \exp\left[a\_\mathbf{x}\left(\frac{T\_\mathcal{g}}{T} - 1\right)\right] & (T\_l \le T \le T\_\mathcal{h}) \\\ \mathbf{x}(T\_\mathcal{h}) & (T \ge T\_\mathcal{h}) \end{cases} \tag{5}$$

where, σ, ε and ε<sup>l</sup> denote the stress, strain and irrecoverable strain, E is elastic modulus. μ and λ are viscosity and retardation time, respectively. C is a coefficient of irrecoverable strain. T, Tl, Tg, T<sup>h</sup> and ax denote the current temperature, low temperature, glassy transition temperature, melting temperature and proportional coefficient, respectively.

Figure 12. Four-element model.

The shear deformation and its recovery behavior were investigated through a double lap joint arrangement at below and above T<sup>g</sup> [27]. Torsional shape memory tests were carried out to characterize the SME, and a torsional device with a CCD camera was used to quantify the parameters of the SME [28]. A series of tension, compression, bending and twisting experiments of TSMPs were performed to indicate the SME; it is shown that the heating rate has an

These experimental findings provide an experimental guidance for future applications, including aerospace, automotive, robotics, and smart actuator, and so on. Some novel experiments and protocols are expected to be designed for characterizing the SME of smart structures in future.

Constitutive models of TSMPs, including shape memory model describing the SME and the thermo-mechanically coupled model describing the internal heat generation caused by

Based on the different deformation mechanisms, different models were constructed to describe the SME of TSMPs, including the rheology model considering the mobility and relaxation and the meso-mechanical model considering the phase transition between the frozen and active phases.

The mobility of chain segments is a classical mechanism to describe the SME, which remarkably depends on ambient temperature. Tobushi et al. [21] think that the shape of TSMPs can be fixed due to the decreased mobility of chain segments with the decrease of temperature, and the shape can be recovered due to the increased mobility of chain segments with the increase of temperature. Therefore, a rheological model was proposed by introducing a slip element into a three-element standard linear visco-elastic model, as shown in Figure 12, and the mobility of chain segments can be expressed as the exponential functions between material parameters

ð Þ Tl ≤ T ≤ T<sup>h</sup>

x ¼ E; μ; λ; C; ε<sup>l</sup> � �

(5)

x Tð Þ<sup>l</sup> ð Þ T ≤ Tl

x Tð Þ<sup>h</sup> ð Þ T ≥ T<sup>h</sup>

where, σ, ε and ε<sup>l</sup> denote the stress, strain and irrecoverable strain, E is elastic modulus. μ and λ are viscosity and retardation time, respectively. C is a coefficient of irrecoverable strain. T, Tl, Tg, T<sup>h</sup> and ax denote the current temperature, low temperature, glassy transition temperature,

Tg <sup>T</sup> � <sup>1</sup> � � � �

xg exp ax

melting temperature and proportional coefficient, respectively.

obvious influence on the start temperature of shape recovery [29].

mechanical deformation, are commented on in this section.

3. Constitutive models

84 Shape-Memory Materials

3.1. Shape memory model

3.1.1. Rheology model

and temperature, as shown in Eq. (5).

8 >>><

>>>:

x Tð Þ¼

To describe the nonlinear behaviors of TSMPs, a one-dimensional nonlinear visco-elastic model was extended from a linear visco-elastic version [30]. However, the extended model provides an overestimation of the responded stress at large strain, and thus the linear model was further modified to reasonably simulate the SME of TSMPs at large strain by introducing new nonlinear evolution equations with stress threshold values into the cooling modulus and irrecoverable strain [31].

It is noted that, even though the mechanical responses at large strain were simulated, the abovementioned models were established at small deformation. Therefore, Diani et al. [32] developed a thermo-mechanical model of TSMPs at finite deformation based on the three element standard linear visco-elastic model [21]. The total deformation gradient is decomposed into elastic and viscous parts. The total Cauchy stress includes the stresses caused by the entropy change and internal energy change, respectively.

Nguyen et al. [33] developed a thermo-visco-elastic model to describe the time-dependent and temperature-dependent deformations of TSMPs by incorporating structural relaxation and stress relaxations. The model can reproduce the strain-temperature response, rate-dependent stress-strain response and some important features of temperature dependent shape memory responses. In the model, a fictive temperature Tf is used to describe the structural relaxation behavior and the structural relaxation time is obtained from the WLF equation, as shown in Eq. (6). The stress relaxation adopts the form of visco-elasticity in the glass transition region and rubbery state, and the modified WLF equation is introduced into the Eyring equation to obtain a modified visco-plastic flow rule for describing the visco-plastic deformation, including the glassy state and rubbery state, see Eq. (7).

$$\tau\_{\rm R}\left(T, T\_f\left(\overline{\delta}^{\rm req}\right)\right) = \tau\_{\rm R\xi} \exp\left[-\frac{\mathcal{C}\_1}{\log e} \left(\frac{\mathcal{C}\_2\left(T - T\_f\right) + T\left(T\_f - T\_{\rm g}^{ref}\right)}{T\left(\mathcal{C}\_2 + T\_f - T\_{\rm g}^{ref}\right)}\right)\right] \tag{6}$$

$$\dot{\gamma}^{\text{v}} = \frac{s\_{\text{y}}}{\sqrt{2} \eta\_{\text{s}\_{\text{f}}}^{\text{ref}}} \frac{T}{Q\_{s}} \exp\left[\frac{\mathbb{C}\_{1}}{\log e} \left(\frac{\mathbb{C}\_{2} \left(T - T\_{f}\right) + T \left(T\_{f} - T\_{\text{g}}^{\text{ref}}\right)}{T \left(\mathbb{C}\_{2} + T\_{f} - T\_{\text{g}}^{\text{ref}}\right)}\right)\right] \text{sinh}\left(\frac{Q\_{s} \left\|\mathbf{s}^{\text{ueq}}\right\|}{T}\right) \tag{7}$$

where τ<sup>R</sup> and τRg are the structural relaxation time and relaxation time at a reference temperature Tref <sup>g</sup> , respectively; C<sup>1</sup> and C<sup>2</sup> are material constants using in the WLF equation. δ neq denotes the nonequilibrium part of the isobaric volumetric deformation. γ\_ <sup>v</sup> and sy denote the effective viscous shear stretch rate and yield strength. Qs is a thermal activation parameter and sneq is the nonequilibrium part of the deviatoric component of Cauchy stress.

where ϕ<sup>f</sup> denotes the volume fraction of frozen phase; σ is the total stress; σ<sup>a</sup> and σ<sup>f</sup> are the stresses in the active phase and frozen phase, respectively; ε is the total strain; and ε<sup>a</sup> and ε<sup>f</sup> are

Based on the meso-mechanical model [44], the thermo-elastic models [45, 46] were constructed to simulate the SME of TSMPs at small deformation and large deformation, respectively. Qi et al. [47] assumed that the TSMPs consist of three phases, including the rubbery phase, initial glassy phase and frozen glassy phase. The volume fraction of each phase is assumed as the function of temperature, as shown in Eq. (11). The volume fraction of rubbery phase ϕ<sup>r</sup> is defined as Eq. (12) during cooling and heating. The volume fraction of rubbery phase transforms into the volume fraction of frozen glassy phase during cooling. It is assumed that the increments in the volume fractions of the initial glassy phase ϕg0 and frozen glassy phases ϕ<sup>T</sup> depend on their relative volume fraction during reheating, as shown in Eq. (12). In the meantime, the corresponding

ϕ<sup>g</sup> þ ϕ<sup>r</sup> ¼ 1, ϕg0 þ ϕ<sup>T</sup> ¼ ϕ<sup>g</sup> (11)

T ¼ ϕrT<sup>r</sup> þ ϕg0Tg0 þ ϕTT<sup>T</sup> (13)

Δϕg, Δϕ<sup>T</sup> <sup>¼</sup> <sup>ϕ</sup><sup>T</sup>

Experiments and Models of Thermo-Induced Shape Memory Polymers

http://dx.doi.org/10.5772/intechopen.78012

87

ϕg0 þ ϕ<sup>T</sup>

Δϕ<sup>g</sup> (12)

ϕg0 þ ϕ<sup>T</sup>

where T is the total stress. Tr, Tg0 and T<sup>T</sup> denote stress in the rubbery phase, frozen phase and

Based on the abovementioned meso-mechanical method with a mixture rule, a threedimensional model was proposed for TSMPs [48], which distinguishes between two phases presenting different properties. The model can reproduce both heating-stretching-cooling and cold drawing shape-fixing procedures and was applied in the simulations from simple uniax-

Pieczyska proposed thermo-mechanically coupled models at finite deformation [8, 19] to reproduce the rate-dependent stress-strain curve and the strain localization behavior. However, this model cannot describe the temperature variation induced by the internal heat generation since the thermo-elastic effect and the visco-plastic dissipation are neglected. To reasonably describe the influence of the internal heat generation on the mechanical behavior of TSMPs, the Helmholtz free energy ψ is decomposed into three parts, that is, the instantaneous elastic free energy

, visco-plastic free energy ψvp and heat free energy ψ<sup>T</sup>, and the stress-strain relationship is

; <sup>B</sup>vp ð Þ¼ ; <sup>T</sup> <sup>ψ</sup><sup>e</sup> <sup>C</sup><sup>e</sup> ð Þþ ; <sup>T</sup> <sup>ψ</sup>vp <sup>B</sup>vp ð Þþ ; <sup>T</sup> <sup>ψ</sup><sup>T</sup>ð Þ <sup>T</sup> (14)

K Tð Þ tr <sup>E</sup><sup>e</sup> j j ð Þ <sup>2</sup> � <sup>3</sup>K Tð Þtr <sup>E</sup><sup>e</sup> ð Þαð Þ <sup>T</sup> � <sup>T</sup><sup>0</sup> (15)

the strains in the active phase and frozen phase, respectively.

stresses in the three phases satisfy with the rule of mixture, see Eq. (13).

<sup>1</sup> <sup>þ</sup> exp ½ � �ð Þ <sup>T</sup> � <sup>T</sup><sup>r</sup> <sup>=</sup><sup>A</sup> , Δϕg0 <sup>¼</sup> <sup>ϕ</sup>g0

ial and biaxial tests to complex loadings of biomedical devices.

derived from the Helmholtz free energy [49], as shown in Eqs. (14)–(17).

0 2 þ 1 2

<sup>ϕ</sup><sup>r</sup> <sup>¼</sup> <sup>1</sup>

initial glassy phase, respectively.

ψe

3.2. Thermo-mechanically coupled model

ψ C<sup>e</sup>

<sup>ψ</sup><sup>e</sup> <sup>E</sup><sup>e</sup> ð Þ¼ ; <sup>T</sup> G Tð Þ <sup>E</sup><sup>e</sup>

Based on the model proposed by Nguyen et al. [33], Li et al. [7] also developed a thermovisco-elastic-visco-plastic model considering the structural relaxation and stress relaxation. The model was used to predict the nonlinear SME of TSMPs programmed by coldcompression below the glassy transition temperature. Chen et al. [34] performed parameter studies on the SME in the conditions of the stress-free recovery and strain-constrained recovery with different loading parameters, including the cooling rate, heating rate, strain rate, anneal time and temperature. The results show that the SME is affected by different mechanisms, including the thermal expansion, structural relaxation and stress relaxation. Chen et al. [35] developed a rheological model by introducing the thermal expansion, structural relaxation and stress relaxation into a standard linear visco-elastic model; the Mooney-Rivlin function and Newton fluid assumptions were used to describe the hyper-elasticity of rubbery state and flow behavior of glassy state during the process of the glass transition, respectively.

Recently, the multibranch models considering the stress relaxation were developed to reasonably capture the SME of TSMPs [16, 36–38]. For considering more complex shape memory behaviors, Xiao et al. [39] proposed a thermo-visco-plastic model at finite deformation to describe the multiple SME and temperature memory effect by introducing the structural relaxation and stress relaxation [39]. Besides, for the purpose of the structural analysis, the linear visco-elastic model [21] was extended to three-dimensional version and was implemented into ABAQUS by using the user material subroutine UMAT to simulate the SME of structures [40–43].

#### 3.1.2. Meso-mechanical model

The meso-mechanical model was firstly proposed by Liu et al. [44] to describe the physical mechanisms of the stress-free recovery and strain-constraint recovery at the pre-deformation strain level of TSMPs. In the model, it is assumed that the TSMPs consist of two extreme phases, including the frozen phase and active phase. The frozen phase is the major phase in the glassy state, where the conformational motion is constrained. In contrast, the active phase exists in the full rubbery state, and the free conformational motion potentially occurs. By changing the ratio of these two phases, the glassy transition in a thermo-mechanical cycle is embodied and thus the shape memory effect can be captured. To quantify the changes of mechanical properties with temperature, the volume fraction of frozen phase is defined as Eq. (8) and can be obtained by fitting the curve of recovery strain. It is assumed that the corresponding stresses in these two phases are equal to σ (see Eq. (9)), and the total strain ε is defined as Eq. (10).

$$\phi\_{\rm f} = 1 - \frac{1}{1 + c\_{\rm f}(T\_{\rm h} - T)^n} \tag{8}$$

$$
\mathfrak{o} = \phi\_{\mathfrak{f}} \mathfrak{o}\_{\mathfrak{f}} + \left(1 - \phi\_{\mathfrak{f}}\right) \mathfrak{o}\_{\mathfrak{u}} \mathfrak{o}\_{\mathfrak{f}} = \mathfrak{o}\_{\mathfrak{a}} = \mathfrak{o} \tag{9}
$$

$$
\mathfrak{e} = \phi\_{\mathfrak{f}} \mathfrak{e}\_{\mathfrak{f}} + \left(\mathbbm{1} - \phi\_{\mathfrak{f}}\right) \mathfrak{e}\_{\mathfrak{a}} \tag{10}
$$

where ϕ<sup>f</sup> denotes the volume fraction of frozen phase; σ is the total stress; σ<sup>a</sup> and σ<sup>f</sup> are the stresses in the active phase and frozen phase, respectively; ε is the total strain; and ε<sup>a</sup> and ε<sup>f</sup> are the strains in the active phase and frozen phase, respectively.

Based on the meso-mechanical model [44], the thermo-elastic models [45, 46] were constructed to simulate the SME of TSMPs at small deformation and large deformation, respectively. Qi et al. [47] assumed that the TSMPs consist of three phases, including the rubbery phase, initial glassy phase and frozen glassy phase. The volume fraction of each phase is assumed as the function of temperature, as shown in Eq. (11). The volume fraction of rubbery phase ϕ<sup>r</sup> is defined as Eq. (12) during cooling and heating. The volume fraction of rubbery phase transforms into the volume fraction of frozen glassy phase during cooling. It is assumed that the increments in the volume fractions of the initial glassy phase ϕg0 and frozen glassy phases ϕ<sup>T</sup> depend on their relative volume fraction during reheating, as shown in Eq. (12). In the meantime, the corresponding stresses in the three phases satisfy with the rule of mixture, see Eq. (13).

$$
\phi\_{\mathbf{g}} + \phi\_{\mathbf{r}} = \mathbf{1}, \ \phi\_{\mathbf{g}0} + \phi\_{\mathbf{T}} = \phi\_{\mathbf{g}} \tag{11}
$$

$$\phi\_{\rm r} = \frac{1}{1 + \exp\left[-(T - T\_{\rm r})/A\right]}, \Delta\phi\_{\rm g0} = \frac{\phi\_{\rm g0}}{\phi\_{\rm g0} + \phi\_{\rm r}} \Delta\phi\_{\rm g'} \,\Delta\phi\_{\rm r} = \frac{\phi\_{\rm r}}{\phi\_{\rm g0} + \phi\_{\rm r}} \Delta\phi\_{\rm g} \tag{12}$$

$$\mathbf{T} = \boldsymbol{\phi}\_{\mathbf{r}} \mathbf{T}\_{\mathbf{r}} + \boldsymbol{\phi}\_{\mathbf{g}0} \mathbf{T}\_{\mathbf{g}0} + \boldsymbol{\phi}\_{\mathbf{T}} \mathbf{T}\_{\mathbf{T}} \tag{13}$$

where T is the total stress. Tr, Tg0 and T<sup>T</sup> denote stress in the rubbery phase, frozen phase and initial glassy phase, respectively.

Based on the abovementioned meso-mechanical method with a mixture rule, a threedimensional model was proposed for TSMPs [48], which distinguishes between two phases presenting different properties. The model can reproduce both heating-stretching-cooling and cold drawing shape-fixing procedures and was applied in the simulations from simple uniaxial and biaxial tests to complex loadings of biomedical devices.

#### 3.2. Thermo-mechanically coupled model

where τ<sup>R</sup> and τRg are the structural relaxation time and relaxation time at a reference temper-

denotes the nonequilibrium part of the isobaric volumetric deformation. γ\_ <sup>v</sup> and sy denote the effective viscous shear stretch rate and yield strength. Qs is a thermal activation parameter and

Based on the model proposed by Nguyen et al. [33], Li et al. [7] also developed a thermovisco-elastic-visco-plastic model considering the structural relaxation and stress relaxation. The model was used to predict the nonlinear SME of TSMPs programmed by coldcompression below the glassy transition temperature. Chen et al. [34] performed parameter studies on the SME in the conditions of the stress-free recovery and strain-constrained recovery with different loading parameters, including the cooling rate, heating rate, strain rate, anneal time and temperature. The results show that the SME is affected by different mechanisms, including the thermal expansion, structural relaxation and stress relaxation. Chen et al. [35] developed a rheological model by introducing the thermal expansion, structural relaxation and stress relaxation into a standard linear visco-elastic model; the Mooney-Rivlin function and Newton fluid assumptions were used to describe the hyper-elasticity of rubbery state and

sneq is the nonequilibrium part of the deviatoric component of Cauchy stress.

flow behavior of glassy state during the process of the glass transition, respectively.

the user material subroutine UMAT to simulate the SME of structures [40–43].

phases are equal to σ (see Eq. (9)), and the total strain ε is defined as Eq. (10).

σ ¼ ϕ<sup>f</sup>

<sup>ϕ</sup><sup>f</sup> <sup>¼</sup> <sup>1</sup> � <sup>1</sup>

ε<sup>f</sup> þ 1 � ϕ<sup>f</sup>

σ<sup>f</sup> þ 1 � ϕ<sup>f</sup>

ε ¼ ϕ<sup>f</sup>

<sup>1</sup> <sup>þ</sup> <sup>c</sup>fð Þ <sup>T</sup><sup>h</sup> � <sup>T</sup> <sup>n</sup> (8)

ε<sup>a</sup> (10)

<sup>σ</sup>a, <sup>σ</sup><sup>f</sup> <sup>¼</sup> <sup>σ</sup><sup>a</sup> <sup>¼</sup> <sup>σ</sup> (9)

Recently, the multibranch models considering the stress relaxation were developed to reasonably capture the SME of TSMPs [16, 36–38]. For considering more complex shape memory behaviors, Xiao et al. [39] proposed a thermo-visco-plastic model at finite deformation to describe the multiple SME and temperature memory effect by introducing the structural relaxation and stress relaxation [39]. Besides, for the purpose of the structural analysis, the linear visco-elastic model [21] was extended to three-dimensional version and was implemented into ABAQUS by using

The meso-mechanical model was firstly proposed by Liu et al. [44] to describe the physical mechanisms of the stress-free recovery and strain-constraint recovery at the pre-deformation strain level of TSMPs. In the model, it is assumed that the TSMPs consist of two extreme phases, including the frozen phase and active phase. The frozen phase is the major phase in the glassy state, where the conformational motion is constrained. In contrast, the active phase exists in the full rubbery state, and the free conformational motion potentially occurs. By changing the ratio of these two phases, the glassy transition in a thermo-mechanical cycle is embodied and thus the shape memory effect can be captured. To quantify the changes of mechanical properties with temperature, the volume fraction of frozen phase is defined as Eq. (8) and can be obtained by fitting the curve of recovery strain. It is assumed that the corresponding stresses in these two

<sup>g</sup> , respectively; C<sup>1</sup> and C<sup>2</sup> are material constants using in the WLF equation. δ

neq

ature Tref

86 Shape-Memory Materials

3.1.2. Meso-mechanical model

Pieczyska proposed thermo-mechanically coupled models at finite deformation [8, 19] to reproduce the rate-dependent stress-strain curve and the strain localization behavior. However, this model cannot describe the temperature variation induced by the internal heat generation since the thermo-elastic effect and the visco-plastic dissipation are neglected. To reasonably describe the influence of the internal heat generation on the mechanical behavior of TSMPs, the Helmholtz free energy ψ is decomposed into three parts, that is, the instantaneous elastic free energy ψe , visco-plastic free energy ψvp and heat free energy ψ<sup>T</sup>, and the stress-strain relationship is derived from the Helmholtz free energy [49], as shown in Eqs. (14)–(17).

$$
\psi(\mathbf{C}^{\mathbf{e}}, \mathbf{B}^{\text{vp}}, T) = \psi^{\mathbf{e}}(\mathbf{C}^{\mathbf{e}}, T) + \psi^{\text{vp}}(\mathbf{B}^{\text{vp}}, T) + \psi^{T}(T) \tag{14}
$$

$$\psi^{\varepsilon}(\mathbf{E}^{\varepsilon},T) = G(T)\left|\mathbf{E}\_{0}^{\varepsilon}\right|^{2} + \frac{1}{2}K(T)\left|\text{tr}(\mathbf{E}^{\varepsilon})\right|^{2} - 3K(T)\text{tr}(\mathbf{E}^{\varepsilon})a(T-T\_{0})\tag{15}$$

$$\psi^{\rm vp}(\lambda^{\rm vp}, T) = \mu\_{\rm R}(T)\lambda\_{\rm L}^{-2} \left[ \left( \frac{\lambda^{\rm vp}}{\lambda\_{\rm L}} \right) \mathbf{x} + \ln \left( \frac{\mathbf{x}}{\sinh \mathbf{x}} \right) \right], \quad \mathbf{x} = \mathcal{L}^{-1} \left( \frac{\lambda^{\rm vp}}{\lambda\_{\rm L}} \right) \tag{16}$$

$$\psi^T(T) = c \left[ (T - T\_0) - T \ln \left( \frac{T}{T\_0} \right) \right] + \mu\_0 - \eta\_0 T \tag{17}$$

are the volume and surface of a specimen. The proportional factor <sup>n</sup> is introduced to reflect the

Experiments and Models of Thermo-Induced Shape Memory Polymers

http://dx.doi.org/10.5772/intechopen.78012

89

Based on the abovementioned constitutive description, a thermo-elasto-visco-plastic model was established at finite deformation to reasonably predict the rate-dependent stress-strain responses and temperature variations, including the temperature drop due to the thermo-elastic effect and

Recent advances in experiments and models of TMPs are reviewed, the main conclusions are

1. The TSMPs exhibit rate-dependent and temperature-dependent mechanical responses, a strong interaction between the internal heat generation and mechanical deformation is observed and strain and temperature distributions are nonuniform in tension. The internal heat generation is contributed by the decreased temperature due to the thermo-elastic

2. The SME of TSMPs in the conditions of the stress-free recovery and strain-constraint recovery can be characterized by the shape recovery ratio, which decreases with the increases of peak strain, holding time after deformation, heating rate and decrease with

3. The shape memory degeneration of TSMPs occurs under cyclic thermo-mechanical loadings and can be reflected by the strain recovery ratio, which gradually decreases with the increase of number of cycles and also depends on the peak strain, deformable temperature,

4. Two types of models have been established, including the shape memory model which describing the SME and the thermo-mechanically coupled model which describing the interaction between the mechanical deformation, internal heat generation and heat exchange. 5. As mentioned earlier, most experiments and models of TSMPs are limited within uniaxial loading and the SME is performed by heating to a certain temperature. The experimental observations on the proportional and nonproportional multiaxial mechanical responses and the SME subjected to shape memory cycles are insufficient, the multiaxial thermo-mechanically coupled model is necessary to be constructed for predicting the SME more accurate. Moreover, the experimental and theoretical investigations on the deformation mechanisms of the multiple

Financial supports by National Natural Science Foundation of China (11572265; 11532010) and

SME and temperature memory effect are necessary to be addressed in future.

Excellent Youth Found of Sichuan Province (2017JQ0019) are acknowledged.

effect and the increased temperature due to the visco-plastic dissipation.

the decreases of loading rate and finish recovery temperature.

recovery temperature and previous mechanical training.

the temperature rise due to the visco-plastic dissipation, as shown in Figures 13 and 14.

proportion of the work converting into heat.

4. Conclusions and remarks

Acknowledgements

below:

where C<sup>e</sup> , Bvp denote the elastic right Cauchy-Green tensor and visco-plastic left Cauchy-Green tensor, respectively. E<sup>e</sup> and E<sup>e</sup> <sup>0</sup> are the Hencky's logarithmic strain and its deviatoric part, respectively. T<sup>0</sup> is the initial temperature. λvp and λ<sup>L</sup> denote the visco-plastic stretch and limiting stretch, respectively. u<sup>0</sup> and η<sup>0</sup> denote the initial internal energy and initial entropy, respectively. μR, G and K denote the temperature-dependent hardening modulus, shear modulus and bulk modulus, respectively. The parameter c denotes the specific heat, and the symbol L�<sup>1</sup> denotes the inverse of Langevin function.

The heat equilibrium equation of the internal heat generation and heat exchange is derived based on an average temperature filed along the sample, as shown in Eq. (18).

$$
\omega\_{\rm eff} \dot{T} = \omega \Gamma\_{\rm eff} + \frac{h(T\_0 - T)S}{V} \tag{18}
$$

where h is the heat exchange coefficient of ambient media, which is a constant if without forced convection. ceff and Γeff are the equivalent specific heat and dissipation, respectively, S and V

Figure 13. Experimental and simulated stress-strain curves at different strain rates: (a) 1.4%/s; (b) 0.7%/s; and (c) 0.35%/s.

Figure 14. Experimental and simulated temperature variation at different strain rates: (a) 1.4%/s; (b) 0.7%/s; and (c) 0.35%/s.

are the volume and surface of a specimen. The proportional factor <sup>n</sup> is introduced to reflect the proportion of the work converting into heat.

Based on the abovementioned constitutive description, a thermo-elasto-visco-plastic model was established at finite deformation to reasonably predict the rate-dependent stress-strain responses and temperature variations, including the temperature drop due to the thermo-elastic effect and the temperature rise due to the visco-plastic dissipation, as shown in Figures 13 and 14.

## 4. Conclusions and remarks

<sup>ψ</sup>vp <sup>λ</sup>vp ð Þ¼ ; <sup>T</sup> <sup>μ</sup>Rð Þ <sup>T</sup> <sup>λ</sup><sup>L</sup>

Green tensor, respectively. E<sup>e</sup> and E<sup>e</sup>

L�<sup>1</sup> denotes the inverse of Langevin function.

where C<sup>e</sup>

88 Shape-Memory Materials

0.35%/s.

<sup>2</sup> λvp λL 

<sup>ψ</sup><sup>T</sup>ð Þ¼ <sup>T</sup> c Tð Þ� � <sup>T</sup><sup>0</sup> <sup>T</sup> ln <sup>T</sup>

based on an average temperature filed along the sample, as shown in Eq. (18).

<sup>c</sup>effT\_ <sup>¼</sup> <sup>ω</sup>Γeff <sup>þ</sup>

<sup>x</sup> <sup>þ</sup> ln <sup>x</sup>

part, respectively. T<sup>0</sup> is the initial temperature. λvp and λ<sup>L</sup> denote the visco-plastic stretch and limiting stretch, respectively. u<sup>0</sup> and η<sup>0</sup> denote the initial internal energy and initial entropy, respectively. μR, G and K denote the temperature-dependent hardening modulus, shear modulus and bulk modulus, respectively. The parameter c denotes the specific heat, and the symbol

The heat equilibrium equation of the internal heat generation and heat exchange is derived

where h is the heat exchange coefficient of ambient media, which is a constant if without forced convection. ceff and Γeff are the equivalent specific heat and dissipation, respectively, S and V

Figure 13. Experimental and simulated stress-strain curves at different strain rates: (a) 1.4%/s; (b) 0.7%/s; and (c) 0.35%/s.

Figure 14. Experimental and simulated temperature variation at different strain rates: (a) 1.4%/s; (b) 0.7%/s; and (c)

sinh x

T0

h Tð Þ <sup>0</sup> � T S

, Bvp denote the elastic right Cauchy-Green tensor and visco-plastic left Cauchy-

, x <sup>¼</sup> <sup>L</sup>�<sup>1</sup> <sup>λ</sup>vp

<sup>0</sup> are the Hencky's logarithmic strain and its deviatoric

λL 

þ u<sup>0</sup> � η0T (17)

<sup>V</sup> (18)

(16)

Recent advances in experiments and models of TMPs are reviewed, the main conclusions are below:


## Acknowledgements

Financial supports by National Natural Science Foundation of China (11572265; 11532010) and Excellent Youth Found of Sichuan Province (2017JQ0019) are acknowledged.

## Author details

Qianhua Kan<sup>1</sup> \*, Jian Li<sup>2</sup> , Guozheng Kang1 and Zebin Zhang<sup>2</sup>

\*Address all correspondence to: qianhuakan@foxmail.com

1 State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu,

P. R. China

2 School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, P. R. China

[11] Tobushi H, Hara H, Yamada E, et al. Thermomechanical properties in a thin film of shape memory polymer of polyurethane series. Smart Materials & Structures. 1996;2716(4):483.

Experiments and Models of Thermo-Induced Shape Memory Polymers

http://dx.doi.org/10.5772/intechopen.78012

91

[12] Atli B, Gandhi F. Thermomechanical characterization of shape memory polymers. Journal of Intelligent Material Systems & Structures. 2009;17(20):7002-7011. DOI: 10.1117/12.715248

[13] Cui J, Kratz K, Lendlein A. Adjusting shape-memory properties of amorphous polyether urethanes and radio-opaque composites thereof by variation of physical parameters during programming. Smart Materials & Structures. 2010;19(6):065019. DOI: 10.1088/0964-

[14] Hu JL, Ji FL, Wong YW. Dependency of the shape memory properties of a polyurethane upon thermomechanical cyclic conditions. Polymer International. 2005;54(3):600-605. DOI:

[15] Volk B L, Lagoudas D C, Chen Y C, et al. Analysis of the finite deformation response of shape memory polymers: I. Thermomechanical characterization. Smart Material Struc-

[16] Zhang C, Gou X, Xiao R. Controllable shape-memory recovery regions in polymers through mechanical programming. Journal of Applied Polymer Science. 2017;135(8). DOI: 10.1002/

[17] Mcclung AJW, Tandon GP, Baur JW. Deformation rate-, hold time-, and cycle-dependent shape-memory performance of Veriflex-E resin. Mechanics of Time-Dependent Materials.

[18] Azra C, Plummer CJG, Månson JAE. Isothermal recovery rates in shape memory polyurethanes. Smart Materials & Structures. 2011;20(8):082002. DOI: 10.1088/0964-1726/20/8/

[19] Pieczyska EA, Staszczak M, Maj M, et al. Investigation of thermomechanical couplings, strain localization and shape memory properties in a shape memory polymer subjected to loading at various strain rates. Smart Materials & Structures. 2016;25(8):085002. DOI:

[20] Pieczyska EA, Staszczak M, Kowalczyk-Gajewska K, et al. Experimental and numerical investigation of yielding phenomena in a shape memory polymer subjected to cyclic tension at various strain rates. Polymer Testing. 2017;60:333-342. DOI: 10.1016/j.polymertesting.

[21] Tobushi H, Hashimoto T, Hayashi S, et al. Thermomechanical constitutive modeling in shape memory polymer of polyurethane series. Journal of Intelligent Material Systems

[22] Schmidt C, Neuking K, Eggeler G. Functional fatigue of shape memory polymers. Advanced Engineering Materials. 2010;10(10):922-927. DOI: 10.1002/adem.200800213

and Structures. 1997;8(8):711-718. DOI: 10.1177/1045389X9700800808

tures. 2010;19(7):75005-75014(10). DOI: 10.1088/0964-1726/19/7/075005

2013;17(1):39-52. DOI: 10.1007/s11043-011-9157-6

10.1088/0964-1726/25/8/085002

DOI: 10.1117/12.232168

1726/19/6/065019

10.1002/pi.1745

app.45909

082002

2017.04.014

## References


[11] Tobushi H, Hara H, Yamada E, et al. Thermomechanical properties in a thin film of shape memory polymer of polyurethane series. Smart Materials & Structures. 1996;2716(4):483. DOI: 10.1117/12.232168

Author details

90 Shape-Memory Materials

\*, Jian Li<sup>2</sup>

10.1016/S1369-7021(07)70047-0

j.pmatsci.2011.03.001

\*Address all correspondence to: qianhuakan@foxmail.com

tion. 2002;41(12):2034-2057. DOI: 10.1007/978-3-642-12359-7

37(12):1720-1763. DOI: 10.1016/j.progpolymsci.2012.06.001

of Solids. 2011;59(6):1231-1250. DOI: 10.1016/j.jmps.2011.03.001

Structures. 2015;24(4):045043. DOI: 10.1088/0964-1726/24/4/045043

Testing. 2016;51:82-92. DOI: 10.1016/j.polymertesting.2016.03.003

37(26):5781-5793. DOI: 10.1016/S0032-3861(96)00442-9

53(1):130-152. DOI: 10.1080/15583724.2012.751922

, Guozheng Kang1 and Zebin Zhang<sup>2</sup>

1 State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu,

2 School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, P. R. China

[1] Lendlein A, Kelch S. Shape-memory polymers. Angewandte Chemie International Edi-

[2] Hager MD, Bode S, Weber C, et al. Shape memory polymers: Past, present and future developments. Progress in Polymer Science. 2015;49-50:3-33. DOI: 10.1016/j.progpolymsci.2015.04.002

[3] Behl M, Lendlein A. Shape-memory polymers. Materials Today. 2007;10(4):20-28. DOI:

[4] Leng JS, Lan X, Liu Y, et al. Shape-memory polymers and their composites: Stimulus methods and applications. Progress in Materials Science. 2011;56(7):1077-1135. DOI: 10.1016/

[5] Hu J, Zhu Y, Huang H, et al. Recent advances in shape–memory polymers: Structure, mechanism, functionality, modeling and applications. Progress in Polymer Science. 2012;

[6] Nguyen TD. Modeling shape-memory behaviour of polymers. Polymer Reviews. 2013;

[7] Li G, Xu W. Thermomechanical behaviour of thermoset shape memory polymer programmed by cold-compression: Testing and constitutive modeling. Journal of the Mechanics & Physics

[8] Pieczyska EA, Maj M, Kowalczykgajewska K, et al. Thermomechanical properties of polyurethane shape memory polymer-experiment and modelling. Smart Materials &

[9] Zhang ZX, He ZZ, Yang JH, et al. Crystallization controlled shape memory behaviors of dynamically vulcanized poly (l-lactide) /poly (ethylene vinyl acetate) blends. Polymer

[10] Kim BK, Sang YL, Mao X. Polyurethane having shape memory effect. Polymer. 1996;

Qianhua Kan<sup>1</sup>

P. R. China

References


[23] Schmidt C, Chowdhury AMS, Neuking K, et al. Studies on the cycling, processing and programming of an industrially applicable shape memory polymer Tecoflex(R) (or TFX EG 72D). Journal of the Royal Society of Medicine. 2011;80(9):544-546. DOI: 10.1177/ 0954008311405245

[36] Westbrook KK, Kao PH, Castro F, et al. A 3D finite deformation constitutive model for amorphous shape memory polymers: A multi-branch modeling approach for nonequilibrium relaxation processes. Mechanics of Materials. 2011;43(12):853-869. DOI:

Experiments and Models of Thermo-Induced Shape Memory Polymers

http://dx.doi.org/10.5772/intechopen.78012

93

[37] Yu K, Mcclung AJW, Tandon GP, et al. A thermomechanical constitutive model for an epoxy based shape memory polymer and its parameter identifications. Mechanics of

[38] Li Y, He Y, Liu Z. A viscoelastic constitutive model for shape memory polymers based on multiplicative decompositions of the deformation gradient. International Journal of Plas-

[39] Xiao R, Guo J, Nguyen TD. Modeling the multiple shape memory effect and temperature memory effect in amorphous polymers. RSC Advances. 2014;5(1):416-423. DOI: 10.1039/

[40] Zhou B, Liu Y, Leng J. Finite element analysis on thermo-mechanical behaviour of styrenebased shape memory polymers. Acta Polymerica Sinica. 2009;009(6):525-529. DOI: 10.3321/

[41] Shi G, Yang Q, He X, et al. A three-dimensional constitutive equation and finite element method implementation for shape memory polymers. Computer Modeling in Engineer-

[42] Shi GH, Yang QS, He XQ. Analysis of intelligent hinged shell structures: Deployable deformation and shape memory effect. Smart Materials & Structures. 2013;22(12):126-

[43] Liu YF, Wu JL, Zhang JX, et al. Feasible evaluation of the Thermo-mechanical properties of shape memory polyurethane for orthodontic Archwire. Journal of Medical & Biological

[44] Liu Y, Gall K, Dunn ML, et al. Thermomechanics of shape memory polymers: Uniaxial experiments and constitutive modeling. International Journal of Plasticity. 2006;22(2):279-

[45] Chen YC, Lagoudas DCA. Constitutive theory for shape memory polymers. Part I: Large deformations. Journal of the Mechanics & Physics of Solids. 2008;56:1752-1765. DOI:

[46] Chen YC, Lagoudas DC. A constitutive theory for shape memory polymers. Part II : A linearized model for small deformations. Journal of the Mechanics and Physics of Solids.

[47] Qi HJ, Nguyen TD, Castro F, et al. Finite deformation thermo-mechanical behaviour of thermally induced shape memory polymers. Journal of the Mechanics & Physics of Solids.

ing & Sciences. 2013;90(5):339-358. DOI: 10.3970/cmes.2013.090.339

Engineering. 2017;37(5):666-674. DOI: 10.1007/s40846-017-0263-z

2008;56(5):1766-1778. DOI: 10.1016/j.jmps.2007.12.004

2008;56(5):1730-1751. DOI: 10.1016/j.jmps.2007.12.002

Time-Dependent Materials. 2014;18(2):453-474. DOI: 10.1007/s11043-014-9237-5

ticity. 2017;91:300-317. DOI: 10.1016/j.ijplas.2017.04.004

10.1016/j.mechmat.2011.09.004

c4ra11412d

j.issn:1000-3304.2009.06.005

132. DOI: 10.1088/0964-1726/22/12/125018

313. DOI: 10.1016/j.ijplas.2005.03.004

10.1016/j.jmps.2007.12.005


[36] Westbrook KK, Kao PH, Castro F, et al. A 3D finite deformation constitutive model for amorphous shape memory polymers: A multi-branch modeling approach for nonequilibrium relaxation processes. Mechanics of Materials. 2011;43(12):853-869. DOI: 10.1016/j.mechmat.2011.09.004

[23] Schmidt C, Chowdhury AMS, Neuking K, et al. Studies on the cycling, processing and programming of an industrially applicable shape memory polymer Tecoflex(R) (or TFX EG 72D). Journal of the Royal Society of Medicine. 2011;80(9):544-546. DOI: 10.1177/

[24] Mogharebi S, Kazakeviciute-Makovska R, Steeb H, et al. On the cyclic material stability of shape memory polymer. Materialwissenschaft Und Werkstofftechnik. 2013;44(6):521-526.

[25] Zhang Z, Li J, Chen K, et al. Experimental observation on the thermo-mechanically cyclic deformation behaviour of shape memory polyurethane. Gongneng Cailiao/journal of Functional Materials. 2017;48(5):05174-05179. DOI: 10.3969/j.issn.1001-9731.2017.05.032 [26] Wornyo E, Gall K, Yang F, et al. Nanoindentation of shape memory polymer networks.

[27] Khan F, Koo JH, Monk D, et al. Characterization of shear deformation and strain recovery behaviour in shape memory polymers. Polymer Testing. 2008;27(4):498-503. DOI: 10.1016/

[28] Diani J, Frédy C, Gilormini P, et al. A torsion test for the study of the large deformation recovery of shape memory polymers. Polymer Testing. 2011;30(3):335-341. DOI: 10.1016/j.

[29] Du H, Liu L, Zhang F, et al. Thermal-mechanical behaviour of styrene-based shape memory polymer tubes. Polymer Testing. 2017;57:119-125. DOI: 10.1016/j.polymertesting.2016.11.011

[30] Tobushi H, Okumura K, Hayashi S, et al. Thermomechanical constitutive model of shape memory polymer. Mechanics of Materials. 2001;33(10):545-554. DOI: 10.1016/S0167-6636

[31] Li J, Dong SY, Kan QH, et al. A Thermo-mechanical constitutive model of glassy shape memory polymers. Applied Mechanics & Materials. 2016;853:96-100. DOI: 10.4028/www.

[32] Diani J, Liu Y, Gall K. Finite strain 3D thermoviscoelastic constitutive model for shape memory polymers. Polymer Engineering & Science. 2006;46(4):486-492. DOI: 10.1002/pen.20497

[33] Nguyen TD, Qi HJ, Castro F, et al. A thermoviscoelastic model for amorphous shape memory polymers: Incorporating structural and stress relaxation. Journal of the Mechan-

[34] Chen X, Nguyen TD. Influence of thermoviscoelastic properties and loading conditions on the recovery performance of shape memory polymers. Mechanics of Materials. 2011;43(3):

[35] Chen J, Liu L, Liu Y, et al. Thermoviscoelastic shape memory behaviour for epoxy-shape memory polymer. Smart Materials and Structures. 2014;23(5):055025. DOI: 10.1088/0964-

ics and Physics of Solids. 2008;56(9):2792-2814. DOI: 10.1016/j.jmps.2008.04.007

Polymer. 2007;48(11):3213-3225. DOI: 10.1016/j.polymer.2007.03.029

0954008311405245

92 Shape-Memory Materials

DOI: 10.1002/mawe.201300023

j.polymertesting.2008.02.006

polymertesting.2011.01.008

scientific.net/AMM.853.96

1726/23/5/055025

127-138. DOI: 10.1016/j.mechmat.2011.01.001

(01)00075-8


[48] Boatti E, Scalet G, Auricchio F. A three-dimensional finite-strain phenomenological model for shape-memory polymers: Formulation, numerical simulations, and comparison with experimental data. International Journal of Plasticity. 2016;83:153-177. DOI: 10.1016/j. ijplas.2016.04.008

**Chapter 6**

**Provisional chapter**

**Shape Memory Hydrogels Based on Noncovalent**

**Shape Memory Hydrogels Based on Noncovalent** 

DOI: 10.5772/intechopen.78013

Shape memory polymers (SMPs) are polymeric materials that are capable of fixing temporary shape and recovering the permanent shape in response to external stimuli. In particular, supramolecular interactions and dynamic covalent bond have recently been introduced as temporary switches to construct supramolecular shape memory hydrogels (SSMHs), arising as promising materials since they can exhibit excellent cycled shape memory behavior at room temperature. On the other hand, hydrogels, conventionally, are flexible but sometimes extremely soft, and they can be easily damaged under external force, which could limit their long-time application. Therefore, self-healing hydrogels that can be rapidly auto-repaired when the damage occurs have been recently developed to solve this problem. These materials present more than one triggering stimulus that can be used to induce the shape memory and self-healing effect. These driven forces can be originated from hydrogen bonds, hydrophobic interactions, and reversible covalent bonds, among others. Beyond all these, hybrid organic-inorganic interactions represent an interesting possibility due to their versatility and favorable properties that allow the fabrication of multiresponsive hydrogels. In this chapter, shape memory hydrogels based on noncovalent interactions are described.

**Keywords:** shape memory, hydrogels, supramolecular interactions, self-healing,

Hydrogels are three-dimensional soft networks formed by physical and/or chemical crosslinking of hydrophilic polymers, which are able to swell absorbing and retaining a substantial

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Interactions**

**Interactions**

José Luis Vilas

José Luis Vilas

**Abstract**

smart materials

**1. Introduction**

Leire Ruiz-Rubio, Leyre Pérez-Álvarez,

Leire Ruiz-Rubio, Leyre Pérez-Álvarez,

http://dx.doi.org/10.5772/intechopen.78013

Beñat Artetxe, Juan M. Gutiérrez-Zorrilla and

Beñat Artetxe, Juan M. Gutiérrez-Zorrilla and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

[49] Li J, Kan Qnnnnn Kang G, et al. Thermo-mechanically coupled thermo-elasto-visco-plastic modeling of thermo-induced shape memory polyurethane at finite deformation. Acta Mechanica Solida Sinica. 2018;31(2):141-160. DOI: 10.1007/s10338-018-0022-x

#### **Shape Memory Hydrogels Based on Noncovalent Interactions Shape Memory Hydrogels Based on Noncovalent Interactions**

DOI: 10.5772/intechopen.78013

Leire Ruiz-Rubio, Leyre Pérez-Álvarez, Beñat Artetxe, Juan M. Gutiérrez-Zorrilla and José Luis Vilas Leire Ruiz-Rubio, Leyre Pérez-Álvarez, Beñat Artetxe, Juan M. Gutiérrez-Zorrilla and José Luis Vilas

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78013

#### **Abstract**

[48] Boatti E, Scalet G, Auricchio F. A three-dimensional finite-strain phenomenological model for shape-memory polymers: Formulation, numerical simulations, and comparison with experimental data. International Journal of Plasticity. 2016;83:153-177. DOI: 10.1016/j.

[49] Li J, Kan Qnnnnn Kang G, et al. Thermo-mechanically coupled thermo-elasto-visco-plastic modeling of thermo-induced shape memory polyurethane at finite deformation. Acta

Mechanica Solida Sinica. 2018;31(2):141-160. DOI: 10.1007/s10338-018-0022-x

ijplas.2016.04.008

94 Shape-Memory Materials

Shape memory polymers (SMPs) are polymeric materials that are capable of fixing temporary shape and recovering the permanent shape in response to external stimuli. In particular, supramolecular interactions and dynamic covalent bond have recently been introduced as temporary switches to construct supramolecular shape memory hydrogels (SSMHs), arising as promising materials since they can exhibit excellent cycled shape memory behavior at room temperature. On the other hand, hydrogels, conventionally, are flexible but sometimes extremely soft, and they can be easily damaged under external force, which could limit their long-time application. Therefore, self-healing hydrogels that can be rapidly auto-repaired when the damage occurs have been recently developed to solve this problem. These materials present more than one triggering stimulus that can be used to induce the shape memory and self-healing effect. These driven forces can be originated from hydrogen bonds, hydrophobic interactions, and reversible covalent bonds, among others. Beyond all these, hybrid organic-inorganic interactions represent an interesting possibility due to their versatility and favorable properties that allow the fabrication of multiresponsive hydrogels. In this chapter, shape memory hydrogels based on noncovalent interactions are described.

**Keywords:** shape memory, hydrogels, supramolecular interactions, self-healing, smart materials

## **1. Introduction**

Hydrogels are three-dimensional soft networks formed by physical and/or chemical crosslinking of hydrophilic polymers, which are able to swell absorbing and retaining a substantial

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

amount of water [1]. Hydrogels have been intensively studied due to their relevant properties, such as their similarity to body tissues, low surface friction, ability to encapsulate and release (molecules, ions, cells), appropriate morphology for cell proliferation and stimuli-responsive properties. This stimuli-responsiveness allows hydrogels to be programmed to vary spatially and/or temporally their properties as response against external changes. Different external triggers have been deeply studied along the last years to induce reversible hydrogel-solution or swollen-collapsed transitions, such as pH, temperature, radiation, redox reactions, or chemical triggers [2]. As a consequence of these switchable properties, these materials can behave as actuators or sensors, and therefore, they have been intensively investigated in the last decades in a great variety of fields, among which it is worth to highlight, biomedicine, agriculture and wastewater treatment [3]. Currently, hydrogels are being actively commercialized in all those application fields. However, hydrogels generally show poor mechanical properties, and consequently, mechanical damages and cracks limit their correct function over a long period of time, which is especially problematic for biomedical applications. For this reason, nowadays mechanically more stable materials, such as ceramics or metals, are preferred in this area. Thus, an interesting approach to exploit the full potential of hydrogels would be to promote their self-healing and shape memory properties, which are well known for conventional materials or even polymers but nowadays continues being a challenging issue for hydrogels [4].

> chain (which is one of the most used strategies for hydrophobic SMPs) because they may dissolve. Thus, more elaborated approaches have been developed, such as hydrogels in which hydrophobic crystallizable side chains have been grafted to hydrophilic polymer networks to act as temperature-sensitive temporary crosslinking [9]. However, due to the easy permeation by small molecules and light permeability of hydrogels on their swollen state, in contrast to hydrophobic shape memory polymers, stimuli different to temperature, such as light, [10] pH, [11] or ions [12] can be easily used. When molecular switches reply to more than one stimulus, multishape memory effect can be addressed inducing multiple

Shape Memory Hydrogels Based on Noncovalent Interactions

http://dx.doi.org/10.5772/intechopen.78013

97

**Figure 1.** Schematic representation of (A) self-healing and (B) shape memory effects for hydrogels.

Therefore, self-healing and shape-memory are both originated from the same switchable interactions. In addition to the classical approach that involves the use of crystallizable side chains, these temporary linkers could be dynamic covalent bonds or supramolecular interactions, such as hydrogen bonding, host-guest recognition, or metal-ligand coordination. This chapter reviews the last advances in the strategies in which supramolecular interactions have been used to fix the temporary shape in the quest for obtaining SMH. The interactions can be properly employed in the efficient design of hydrogels for advanced applications and new functionalities that would display high impact in fields like biomedicine. In this sense, sensors for diagnosis, drug delivery systems for controlled and minimal invasive implantation, self-tightening degradable sutures, devices for easy in vitro growth and manipulation of cells, or materials for 3D printing of biomedical devices and soft tissue engineering, among others, are expected to be soon improved by the development of self-healing and shape memory hydrogels. Response time is a key factor in the design of new and effective self-healing and shape memory hydrogels. On the one hand, hydrogels with slow SME may be promising materials for medical implants, in order to

actions on the hydrogels [13].

Self-healing is one of the most fascinating functions encountered in nature, and it represents the ability of a material to regenerate and repair itself after damage. This property is based on reversible chemical or physical interactions that quickly and efficiently are reformed within the structure of the hydrogels, and they would allow to increasing the working lifespan and application frame of hydrogels [5]. A closely related but different property is that so-called shape memory effect (SME), which represents the nonisotropic response of the hydrogel network against changes in the medium. These materials constitute the growing family of shape memory hydrogels (SMH). This means that the polymeric network is able to switch spatially their shape without major volume alteration. This more complex effect requires more sophisticated structural and chemical approaches than selfhealing. The SME implies an elastic deformation (programming) of the hydrogels that are temporarily fixed by means of reversible chemical or physical crosslinking. This temporary shape can reverse to the original shape when these molecular switches are turned off (**Figure 1**). So, shape memory effect lets to recover from the programmed temporary shape when the material is exposed to a given external stimulus; [6] typically temperature, but also light, magnetic or electric field response has been successfully developed [7]. Shape memory polymers (SMP) based on pure polymers, blends and composites have been intensively studied for actuators, sensors, microfluidic systems in aerospace technology, vascular grafts and cardiovascular stents in biomedicine, for textile industry applications and consumer care products [8]. However, SME on hydrophilic soft networks entails some additional difficulties that make impossible the direct transfer from the well-known molecular architecture of hydrophobic SMPs because temporary shape fixation requires crosslinks able to remain stable in an aqueous environment. For example, this fixation may not be carried out by crystalline domains from the hydrophilic polymer acting as main

**Figure 1.** Schematic representation of (A) self-healing and (B) shape memory effects for hydrogels.

amount of water [1]. Hydrogels have been intensively studied due to their relevant properties, such as their similarity to body tissues, low surface friction, ability to encapsulate and release (molecules, ions, cells), appropriate morphology for cell proliferation and stimuli-responsive properties. This stimuli-responsiveness allows hydrogels to be programmed to vary spatially and/or temporally their properties as response against external changes. Different external triggers have been deeply studied along the last years to induce reversible hydrogel-solution or swollen-collapsed transitions, such as pH, temperature, radiation, redox reactions, or chemical triggers [2]. As a consequence of these switchable properties, these materials can behave as actuators or sensors, and therefore, they have been intensively investigated in the last decades in a great variety of fields, among which it is worth to highlight, biomedicine, agriculture and wastewater treatment [3]. Currently, hydrogels are being actively commercialized in all those application fields. However, hydrogels generally show poor mechanical properties, and consequently, mechanical damages and cracks limit their correct function over a long period of time, which is especially problematic for biomedical applications. For this reason, nowadays mechanically more stable materials, such as ceramics or metals, are preferred in this area. Thus, an interesting approach to exploit the full potential of hydrogels would be to promote their self-healing and shape memory properties, which are well known for conventional materials or even polymers but nowadays continues being a challenging

Self-healing is one of the most fascinating functions encountered in nature, and it represents the ability of a material to regenerate and repair itself after damage. This property is based on reversible chemical or physical interactions that quickly and efficiently are reformed within the structure of the hydrogels, and they would allow to increasing the working lifespan and application frame of hydrogels [5]. A closely related but different property is that so-called shape memory effect (SME), which represents the nonisotropic response of the hydrogel network against changes in the medium. These materials constitute the growing family of shape memory hydrogels (SMH). This means that the polymeric network is able to switch spatially their shape without major volume alteration. This more complex effect requires more sophisticated structural and chemical approaches than selfhealing. The SME implies an elastic deformation (programming) of the hydrogels that are temporarily fixed by means of reversible chemical or physical crosslinking. This temporary shape can reverse to the original shape when these molecular switches are turned off (**Figure 1**). So, shape memory effect lets to recover from the programmed temporary shape when the material is exposed to a given external stimulus; [6] typically temperature, but also light, magnetic or electric field response has been successfully developed [7]. Shape memory polymers (SMP) based on pure polymers, blends and composites have been intensively studied for actuators, sensors, microfluidic systems in aerospace technology, vascular grafts and cardiovascular stents in biomedicine, for textile industry applications and consumer care products [8]. However, SME on hydrophilic soft networks entails some additional difficulties that make impossible the direct transfer from the well-known molecular architecture of hydrophobic SMPs because temporary shape fixation requires crosslinks able to remain stable in an aqueous environment. For example, this fixation may not be carried out by crystalline domains from the hydrophilic polymer acting as main

issue for hydrogels [4].

96 Shape-Memory Materials

chain (which is one of the most used strategies for hydrophobic SMPs) because they may dissolve. Thus, more elaborated approaches have been developed, such as hydrogels in which hydrophobic crystallizable side chains have been grafted to hydrophilic polymer networks to act as temperature-sensitive temporary crosslinking [9]. However, due to the easy permeation by small molecules and light permeability of hydrogels on their swollen state, in contrast to hydrophobic shape memory polymers, stimuli different to temperature, such as light, [10] pH, [11] or ions [12] can be easily used. When molecular switches reply to more than one stimulus, multishape memory effect can be addressed inducing multiple actions on the hydrogels [13].

Therefore, self-healing and shape-memory are both originated from the same switchable interactions. In addition to the classical approach that involves the use of crystallizable side chains, these temporary linkers could be dynamic covalent bonds or supramolecular interactions, such as hydrogen bonding, host-guest recognition, or metal-ligand coordination. This chapter reviews the last advances in the strategies in which supramolecular interactions have been used to fix the temporary shape in the quest for obtaining SMH. The interactions can be properly employed in the efficient design of hydrogels for advanced applications and new functionalities that would display high impact in fields like biomedicine. In this sense, sensors for diagnosis, drug delivery systems for controlled and minimal invasive implantation, self-tightening degradable sutures, devices for easy in vitro growth and manipulation of cells, or materials for 3D printing of biomedical devices and soft tissue engineering, among others, are expected to be soon improved by the development of self-healing and shape memory hydrogels. Response time is a key factor in the design of new and effective self-healing and shape memory hydrogels. On the one hand, hydrogels with slow SME may be promising materials for medical implants, in order to avoid post-implantation shocks originated by the sudden alterations. On the other hand, fast SME are of great importance for the development of sensors and actuators, such as robotic devices and artificial muscles. Recently, multiple supramolecular SMH combined with self-healing properties have been reported as an evidence of the promising future of this research field [14]. The obtaining of multiple programmed shapes triggered by diverse properties and tailored SME response speed are currently the main challenges in the development of SMH technology that would open opportunities for a wider range of potential applications and value-added properties.

The simplest SME is also referred as dual shape memory effect and corresponds to the case in which only one reversible interaction and thus one temporary shape is fixed in each shape memory cycle. Accordingly, triple shape memory effect corresponds to two reversible and independent interactions occurring in the same hydrogel network. Currently, despite the huge investigation effort made in the last years, still there is a reduced bibliography about

Shape Memory Hydrogels Based on Noncovalent Interactions

http://dx.doi.org/10.5772/intechopen.78013

99

Although noncovalent interactions are weaker than covalent interactions, their importance in polymer science has been shown; in this context, supramolecular shape memory hydrogels based on noncovalent interactions present an arisen importance. The incorporation of noncovalent interactions into hydrogel network could modify the properties of the formed hydrogel. These variations increased the possible applications not only for shape memory effect or a closely related self-healable ability, but also for the development of high tough hydrogels. In **Figure 2**, the most common interactions used in shape memory hydrogels are described such

Hydrogen bond is an electrostatic attraction between donors and acceptors when a hydrogen atom is covalently bound to a highly electronegative atom. These interactions are considered as a key interaction in supramolecular chemistry due to their highly directionality and their relative high strength. In addition, their ability to form dynamic interactions, with a continuous formation/disruption of the bonds by external stimuli, has increased their use as a driving

The addition of moieties capable to form hydrogen bonds dimers in the hydrogel structure has been successfully used to improve the shape memory effect. For example, ureidopyrimidinone (UPy) presents strong self-complementary dimers by a quadruple hydrogen-bonding, [20] and

as hydrogen bonds, metal-ligand interactions, and ion-ion interactions.

**Figure 2.** Reversible interactions for shape memory hydrogels construction.

triple and multishape memory hydrogels.

**2.1. Hydrogen bonding**

force in shape memory hydrogels.

## **2. Mechanism**

Shape memory mechanism in polymers is based on a dual segment material. On the one hand, an elastic polymer network with netpoints is required to define the permanent shape. These netpoints usually are chemical cross-linkings or physical netpoints such as crystalline domains or complexes. In addition, a programming process consisting of the elastic deformation of the sample takes places and additional molecular switches provide temporary crosslinks to reversibly fix the temporary shape of the material. As a result of the application of an external stimulus, usually temperature, molecular switches are disturbed and the polymer chains acquire their initial mobility that leads to a macroscopic movement resulting in the initial shape [15]. In case of thermoresponsive SME polymeric segments with specific thermal transitions like glass transition, melting, or liquid-crystalline phase transition, these transitions can act as molecular switches when temperature is varied.

In order to extend the potential of SMPs as biomaterials, crucial requirements such as biocompatibility, mechanical properties, and biodegradability have promoted the development of the hydrogels with SME. Similar to thermally induced SMPs, supramolecular shape memory hydrogels present cross-linkings that define the network, this is the permanent shape, and stimuli responsive switches, consisting of reversible interactions to fix the temporary shape (**Figure 1**). Thus, shape fixation and recovery demand interactions easy to be broken and formed, while adequate mechanical properties of the material are closely related to the concentration and strength of all the possible kinds of cross-linkings.

The temporary shape can be created by folding, elongation, or compression. The high water uptake in hydrogels gives rise to shape memory materials able of undergoing large deformation between the temporary and permanent states.

Molecular switches, in the case of hydrogels, usually are not part of the main chain forming the polymer network. Typically, are pending moieties such as short crystallizable side chains, [16] specific groups for host-guest interactions, [17] complex-forming groups [18] or groups able to form dynamic bonds [19]. Similar to self-healing process, polymeric segments reorganize and water flows through the polymer network via diffusion, and the kinetics of these process in different states of deformation of the network will govern the global rate of the SME.

The simplest SME is also referred as dual shape memory effect and corresponds to the case in which only one reversible interaction and thus one temporary shape is fixed in each shape memory cycle. Accordingly, triple shape memory effect corresponds to two reversible and independent interactions occurring in the same hydrogel network. Currently, despite the huge investigation effort made in the last years, still there is a reduced bibliography about triple and multishape memory hydrogels.

Although noncovalent interactions are weaker than covalent interactions, their importance in polymer science has been shown; in this context, supramolecular shape memory hydrogels based on noncovalent interactions present an arisen importance. The incorporation of noncovalent interactions into hydrogel network could modify the properties of the formed hydrogel. These variations increased the possible applications not only for shape memory effect or a closely related self-healable ability, but also for the development of high tough hydrogels. In **Figure 2**, the most common interactions used in shape memory hydrogels are described such as hydrogen bonds, metal-ligand interactions, and ion-ion interactions.

### **2.1. Hydrogen bonding**

avoid post-implantation shocks originated by the sudden alterations. On the other hand, fast SME are of great importance for the development of sensors and actuators, such as robotic devices and artificial muscles. Recently, multiple supramolecular SMH combined with self-healing properties have been reported as an evidence of the promising future of this research field [14]. The obtaining of multiple programmed shapes triggered by diverse properties and tailored SME response speed are currently the main challenges in the development of SMH technology that would open opportunities for a wider range of potential

Shape memory mechanism in polymers is based on a dual segment material. On the one hand, an elastic polymer network with netpoints is required to define the permanent shape. These netpoints usually are chemical cross-linkings or physical netpoints such as crystalline domains or complexes. In addition, a programming process consisting of the elastic deformation of the sample takes places and additional molecular switches provide temporary crosslinks to reversibly fix the temporary shape of the material. As a result of the application of an external stimulus, usually temperature, molecular switches are disturbed and the polymer chains acquire their initial mobility that leads to a macroscopic movement resulting in the initial shape [15]. In case of thermoresponsive SME polymeric segments with specific thermal transitions like glass transition, melting, or liquid-crystalline phase transition, these transi-

In order to extend the potential of SMPs as biomaterials, crucial requirements such as biocompatibility, mechanical properties, and biodegradability have promoted the development of the hydrogels with SME. Similar to thermally induced SMPs, supramolecular shape memory hydrogels present cross-linkings that define the network, this is the permanent shape, and stimuli responsive switches, consisting of reversible interactions to fix the temporary shape (**Figure 1**). Thus, shape fixation and recovery demand interactions easy to be broken and formed, while adequate mechanical properties of the material are closely related to the con-

The temporary shape can be created by folding, elongation, or compression. The high water uptake in hydrogels gives rise to shape memory materials able of undergoing large deforma-

Molecular switches, in the case of hydrogels, usually are not part of the main chain forming the polymer network. Typically, are pending moieties such as short crystallizable side chains, [16] specific groups for host-guest interactions, [17] complex-forming groups [18] or groups able to form dynamic bonds [19]. Similar to self-healing process, polymeric segments reorganize and water flows through the polymer network via diffusion, and the kinetics of these process in different states of deformation of the network will govern the global rate of

applications and value-added properties.

tions can act as molecular switches when temperature is varied.

centration and strength of all the possible kinds of cross-linkings.

tion between the temporary and permanent states.

**2. Mechanism**

98 Shape-Memory Materials

the SME.

Hydrogen bond is an electrostatic attraction between donors and acceptors when a hydrogen atom is covalently bound to a highly electronegative atom. These interactions are considered as a key interaction in supramolecular chemistry due to their highly directionality and their relative high strength. In addition, their ability to form dynamic interactions, with a continuous formation/disruption of the bonds by external stimuli, has increased their use as a driving force in shape memory hydrogels.

The addition of moieties capable to form hydrogen bonds dimers in the hydrogel structure has been successfully used to improve the shape memory effect. For example, ureidopyrimidinone (UPy) presents strong self-complementary dimers by a quadruple hydrogen-bonding, [20] and

**Figure 2.** Reversible interactions for shape memory hydrogels construction.

this strong and unidirectional dimerization could induce the shape recovery effect in the hydrogels. These moieties could be added to the hydrogel by a direct substitution on the main chain of the hydrogel, for example poly(vinylalcohol) (PVA) chain [21] or by modifying one of the monomers such as in a triblock copolymer of poly(*N*-ispropylacrylamide-b-ethylene oxide-*N*-isopropylacrylamide) with UPy motifs on some of *N*-isopropylacrylamide monomers and polymerize by reversible addition-fragmentation chain-transfer (RAFT) [22]. Similarly, some authors have used the strong H-bond dimer of diaminotriazine (DAT) present in 2-vinyl-4,6-diamino-1,3,5 triazine groups to construct SMHs that present strong hydrogen bond dimer (**Figure 3**). Liu et al. have copolymerized DAT units with *N,N*-dimethylacrylamide and PEG diacrylate. These hydrogels possessed robust mechanical properties because of the strong double hydrogen bonds (DAT-DAT hydrogen bonds) that could be broken by the protonation of the two amino groups of DAT, being the shape memory of this hydrogels triggered by pH changes in the medium [23].

in the origin of (1) thermally triggered shape memory behavior of collagen-containing hydrogels [25] and (2) near-infrared light induced rapid shape recovery in a (gelatin/graphene oxide)-based hybrid system, among others [26]. This concept has been extensively studied by Willner and collaborators for the fabrication of DNA-acrylamide SMHs. A pH-responsive material containing polymeric chains with self-complementary DNA strands fixed its temporary triangular shape *via* self-assembly at pH = 5, whereas it transformed back to the original quasi-liquid state when pH was increased to 8 [27]. This rational approach was later extended to more complicated systems exhibiting more than one pair of self-complementary DNA strands and exhibiting two pH-dependent temporary states, [28, 29] and as much as three

Shape Memory Hydrogels Based on Noncovalent Interactions

http://dx.doi.org/10.5772/intechopen.78013

101

Host-guest interactions are in the basis of another interesting method to construct SMHs. The supramolecular interactions established between molecular hosts with large cavities and complementary guests that usually exhibit molecular recognition are able to induce a temporary crosslink. Hydrogels can be synthesized by (1) mixing polymers bearing host entities with those containing guest species or (2) copolymerizing monomers functionalized host and guest units. Although different macrocyclic hosts such as cucurbit[n]urils, crown ethers and cyclodextrins have been used to fabricate self-healing hydrogels based on host-guest interactions according to a recent review [31], only the latter have been exploited to date for the

Cyclodextrins (CD) are a family of cyclic oligosaccharides which have been traditionally used in supramolecular chemistry due to their capability to generate host-guest complexes. Typical cyclodextrins contain six (α-CDs), seven (β-CDs), or eight (γ-CDs) glucose units disposed in a ring, and thus, the size of the inner cavity varies accordingly. CDs have been widely used as drug-delivery systems in pharmaceutical applications because they can form inclusion compounds with hydrophobic drugs and become them water-soluble [32]. Analogously, their shape and chemical properties make CDs ideal candidates for the preparation of rotaxanes [33]. Inspired by rotaxane-like systems, Yang's group reported a poly(pseudorotaxane) supramolecular SMH *via* copolymerization of host (α-CD) and guest (PEG) monomers [34]. The use of acrylamide and acrylate comonomers avoided the rapid precipitation of α-CD/ PEG inclusion complexes in the photoinitiated copolymerization process and afforded a mechanically tough physical hydrogel. Following a different synthetic approach, a mixture of poly-β-cyclodextrin and a polymer with adamantine groups in the side chains affords a physical hydrogel with a high self-healing efficiency [35]. Shape memory properties were

the temporary crosslinking arisen from the coordination between carboxylate groups and Fe3+ ions and the methods for recovering the original shape are those that will be discussed more

With regard to hydrogels that display shape memory behavior induced by host-guest interactions, Li, Zhang and collaborators reported a pH sensitive SMH cross-linking β-CD-modified alginate and diethylenetriamine-modified alginate with Ca2+ ions [36]. At high pH values

aqueous solution. The mechanism of

different triggering stimuli [30].

**2.3. Host-guest interactions**

preparation of SSMHs.

added in both systems after being treated with FeCl<sup>3</sup>

specifically in the next section.

A slightly different approach has been described by Chen et al. [24] in which tannic acid (TA), a polyphenol derived from plants which easily forms H-bonds, develops strong multiple hydrogen bonds with poly(vinyl alcohol) (PVA), and they coagulate when they are physically mixed around 60°C and easily obtained hydrogel at room temperature. The strong hydrogen bonds between PVA and TA fix the permanent crosslink, whereas the H-bonds formed between poly(vinyl alcohol) chains, weaker than the PVA-TA H-bonds, are the temporary crosslinks.

Often the described hydrogen bond interactions not only provide a shape memory effect in the hydrogels but also give a self-healing capability to the formed networks.

#### **2.2. Self-assembly processes in biomimetic systems**

The self-assembly process of biomacromolecules can be considered as a specific way to get the hydrogen bonding-based shape memory performance. Formation of triple-helix structures is

**Figure 3.** Hydrogen bond dimer associated to diaminotriazine.

in the origin of (1) thermally triggered shape memory behavior of collagen-containing hydrogels [25] and (2) near-infrared light induced rapid shape recovery in a (gelatin/graphene oxide)-based hybrid system, among others [26]. This concept has been extensively studied by Willner and collaborators for the fabrication of DNA-acrylamide SMHs. A pH-responsive material containing polymeric chains with self-complementary DNA strands fixed its temporary triangular shape *via* self-assembly at pH = 5, whereas it transformed back to the original quasi-liquid state when pH was increased to 8 [27]. This rational approach was later extended to more complicated systems exhibiting more than one pair of self-complementary DNA strands and exhibiting two pH-dependent temporary states, [28, 29] and as much as three different triggering stimuli [30].

### **2.3. Host-guest interactions**

this strong and unidirectional dimerization could induce the shape recovery effect in the hydrogels. These moieties could be added to the hydrogel by a direct substitution on the main chain of the hydrogel, for example poly(vinylalcohol) (PVA) chain [21] or by modifying one of the monomers such as in a triblock copolymer of poly(*N*-ispropylacrylamide-b-ethylene oxide-*N*-isopropylacrylamide) with UPy motifs on some of *N*-isopropylacrylamide monomers and polymerize by reversible addition-fragmentation chain-transfer (RAFT) [22]. Similarly, some authors have used the strong H-bond dimer of diaminotriazine (DAT) present in 2-vinyl-4,6-diamino-1,3,5 triazine groups to construct SMHs that present strong hydrogen bond dimer (**Figure 3**). Liu et al. have copolymerized DAT units with *N,N*-dimethylacrylamide and PEG diacrylate. These hydrogels possessed robust mechanical properties because of the strong double hydrogen bonds (DAT-DAT hydrogen bonds) that could be broken by the protonation of the two amino groups of DAT, being the shape memory of this hydrogels triggered by pH changes in the medium [23]. A slightly different approach has been described by Chen et al. [24] in which tannic acid (TA), a polyphenol derived from plants which easily forms H-bonds, develops strong multiple hydrogen bonds with poly(vinyl alcohol) (PVA), and they coagulate when they are physically mixed around 60°C and easily obtained hydrogel at room temperature. The strong hydrogen bonds between PVA and TA fix the permanent crosslink, whereas the H-bonds formed between poly(vinyl alcohol) chains, weaker than the PVA-TA H-bonds, are the temporary

Often the described hydrogen bond interactions not only provide a shape memory effect in

The self-assembly process of biomacromolecules can be considered as a specific way to get the hydrogen bonding-based shape memory performance. Formation of triple-helix structures is

the hydrogels but also give a self-healing capability to the formed networks.

**2.2. Self-assembly processes in biomimetic systems**

**Figure 3.** Hydrogen bond dimer associated to diaminotriazine.

crosslinks.

100 Shape-Memory Materials

Host-guest interactions are in the basis of another interesting method to construct SMHs. The supramolecular interactions established between molecular hosts with large cavities and complementary guests that usually exhibit molecular recognition are able to induce a temporary crosslink. Hydrogels can be synthesized by (1) mixing polymers bearing host entities with those containing guest species or (2) copolymerizing monomers functionalized host and guest units. Although different macrocyclic hosts such as cucurbit[n]urils, crown ethers and cyclodextrins have been used to fabricate self-healing hydrogels based on host-guest interactions according to a recent review [31], only the latter have been exploited to date for the preparation of SSMHs.

Cyclodextrins (CD) are a family of cyclic oligosaccharides which have been traditionally used in supramolecular chemistry due to their capability to generate host-guest complexes. Typical cyclodextrins contain six (α-CDs), seven (β-CDs), or eight (γ-CDs) glucose units disposed in a ring, and thus, the size of the inner cavity varies accordingly. CDs have been widely used as drug-delivery systems in pharmaceutical applications because they can form inclusion compounds with hydrophobic drugs and become them water-soluble [32]. Analogously, their shape and chemical properties make CDs ideal candidates for the preparation of rotaxanes [33]. Inspired by rotaxane-like systems, Yang's group reported a poly(pseudorotaxane) supramolecular SMH *via* copolymerization of host (α-CD) and guest (PEG) monomers [34]. The use of acrylamide and acrylate comonomers avoided the rapid precipitation of α-CD/ PEG inclusion complexes in the photoinitiated copolymerization process and afforded a mechanically tough physical hydrogel. Following a different synthetic approach, a mixture of poly-β-cyclodextrin and a polymer with adamantine groups in the side chains affords a physical hydrogel with a high self-healing efficiency [35]. Shape memory properties were added in both systems after being treated with FeCl<sup>3</sup> aqueous solution. The mechanism of the temporary crosslinking arisen from the coordination between carboxylate groups and Fe3+ ions and the methods for recovering the original shape are those that will be discussed more specifically in the next section.

With regard to hydrogels that display shape memory behavior induced by host-guest interactions, Li, Zhang and collaborators reported a pH sensitive SMH cross-linking β-CD-modified alginate and diethylenetriamine-modified alginate with Ca2+ ions [36]. At high pH values (11.5), the material can be easily deformed to its temporary phase because the protonation of amino groups from diethylenetriamine prevents the formation of the inclusion complex. Deprotonation at neutral pH allows the system to recover its initial shape. Encouraged by the high recovery ratio (> 95%), the biocompatibility of the polymeric backbone and the physiological pH in which the shape memory process takes place, and the SMH was evaluated as a promising candidate for biomedical applications. The chemical approach was later extended by the same research group to prepare redox-active SMHs. In this case, ferrocene-modified branched polyethylenimine (PEI) was used in combination with β-CD-modified chitosan. The reduced form of the ferrocene (Fe2+) interacts with β-CD and permits the processing of this material into temporary shapes, whereas its oxidation leads to the shape recovery because the positively charged form is excluded from the CD cavity (**Figure 4**) [37].

between positively charged metal cations and negatively charged groups like phosphates or carboxylates. Examples including systems in which the electrostatic interactions have been identified as the origin of the shape memory behavior will be covered in the next section.

Shape Memory Hydrogels Based on Noncovalent Interactions

http://dx.doi.org/10.5772/intechopen.78013

103

Metal-ligand coordination bonds have been applied in a variety of systems that cover from hard Lewis-bases like O-donor ligands in combination with hard Lewis-acids (Fe3+) to N-donor ligands that interact with softer acids (Cu2+, Zn2+). The former strategy has been applied in cross-linked polyacrylamide/polyacrylic acid gels [38–40]. For instance, randomly distributed and physically cross-linked copolymer hydrogels showed high toughness and excellent processability in such a way that they could be fabricated by three-dimensional printing technologies. The metal coordination bonds could be easily removed through the light-induced reduction of the Fe3+ in the presence of citric acid or protonation of carboxylate groups under acidic pH. Conversely, chemical crosslink afforded a controllable self-deforming SMH: the original shape can be gradually modified as a function of the pH, whereas the transition-metal triggered shape memory behavior starts when the temporary form at basic pH is fixed by its immersion in an aqueous solution containing Fe3+ ions. Shape recovery takes

When it comes to N-donor ligands pyridine, imidazole and cyanide groups have been employed with redox active Cu2+ and nonactive Zn2+ ions to lock the temporary shape. For redox sensitive Cu2+-pyridine bonds (**Figure 5**), the reduction to Cu<sup>+</sup> *via* sodium metabisulphite was used as the external stimulus required to recover the original shape through a process that involved not only the cited shape memory behavior, but also changes in the color and mechanical properties of the material [41]. On the contrary, the polyacrylate chains with

**Figure 5.** Schematic representation of the SME in redox-sensitive hydrogels based on metal-coordination bonds between

concentration in

place in a controllable way by sequential steps that imply the increase of H<sup>+</sup>

the aqueous media.

copper cations and pyridine groups.

Moving a step forward, the use of two different kinds of inclusion complexes acting simultaneously resulted in a SSMH with excellent self-healing and expansion-contraction properties [17]. Both ferrocene and adamantine guests and β-CD hosts were attached in polyacrylamidebased main chains to generate a dual temporary crosslinks. Oxidation of ferrocene groups leads to not only the shape memory behavior, but also to the expansion of the hydrogel. It is worth noting that different temporary shapes can be fixed through mechanical stress applied on the oxidized form taking advantage of the lability of β-CD/adamantine interactions.

### **2.4. Metal-ligand coordination bonds**

This approach is based on the interactions established between the functional oxygen- or nitrogen-donor groups of the polymeric chains that act as ligands toward the transition metal ions that have been incorporated into the system. Coordination bonds are able to fix the temporary shape, whereas their removal by external chelating agent, the action of a reducing species and light- or electrically driven reactions leads back to the original state of the hydrogel. The addition of colorful, redox-, magnetically- and catalytically active transition metal cations can also confer the polymeric material with additional functionalities. It is worth noting that the temporary interactions could often show strong contributions from the electrostatic forces

**Figure 4.** Schematic representation of the SME in redox-sensitive hydrogels based on host-guest interactions between ferrocene and CD groups.

between positively charged metal cations and negatively charged groups like phosphates or carboxylates. Examples including systems in which the electrostatic interactions have been identified as the origin of the shape memory behavior will be covered in the next section.

(11.5), the material can be easily deformed to its temporary phase because the protonation of amino groups from diethylenetriamine prevents the formation of the inclusion complex. Deprotonation at neutral pH allows the system to recover its initial shape. Encouraged by the high recovery ratio (> 95%), the biocompatibility of the polymeric backbone and the physiological pH in which the shape memory process takes place, and the SMH was evaluated as a promising candidate for biomedical applications. The chemical approach was later extended by the same research group to prepare redox-active SMHs. In this case, ferrocene-modified branched polyethylenimine (PEI) was used in combination with β-CD-modified chitosan. The reduced form of the ferrocene (Fe2+) interacts with β-CD and permits the processing of this material into temporary shapes, whereas its oxidation leads to the shape recovery because the

Moving a step forward, the use of two different kinds of inclusion complexes acting simultaneously resulted in a SSMH with excellent self-healing and expansion-contraction properties [17]. Both ferrocene and adamantine guests and β-CD hosts were attached in polyacrylamidebased main chains to generate a dual temporary crosslinks. Oxidation of ferrocene groups leads to not only the shape memory behavior, but also to the expansion of the hydrogel. It is worth noting that different temporary shapes can be fixed through mechanical stress applied on the oxidized form taking advantage of the lability of β-CD/adamantine interactions.

This approach is based on the interactions established between the functional oxygen- or nitrogen-donor groups of the polymeric chains that act as ligands toward the transition metal ions that have been incorporated into the system. Coordination bonds are able to fix the temporary shape, whereas their removal by external chelating agent, the action of a reducing species and light- or electrically driven reactions leads back to the original state of the hydrogel. The addition of colorful, redox-, magnetically- and catalytically active transition metal cations can also confer the polymeric material with additional functionalities. It is worth noting that the temporary interactions could often show strong contributions from the electrostatic forces

**Figure 4.** Schematic representation of the SME in redox-sensitive hydrogels based on host-guest interactions between

positively charged form is excluded from the CD cavity (**Figure 4**) [37].

**2.4. Metal-ligand coordination bonds**

102 Shape-Memory Materials

ferrocene and CD groups.

Metal-ligand coordination bonds have been applied in a variety of systems that cover from hard Lewis-bases like O-donor ligands in combination with hard Lewis-acids (Fe3+) to N-donor ligands that interact with softer acids (Cu2+, Zn2+). The former strategy has been applied in cross-linked polyacrylamide/polyacrylic acid gels [38–40]. For instance, randomly distributed and physically cross-linked copolymer hydrogels showed high toughness and excellent processability in such a way that they could be fabricated by three-dimensional printing technologies. The metal coordination bonds could be easily removed through the light-induced reduction of the Fe3+ in the presence of citric acid or protonation of carboxylate groups under acidic pH. Conversely, chemical crosslink afforded a controllable self-deforming SMH: the original shape can be gradually modified as a function of the pH, whereas the transition-metal triggered shape memory behavior starts when the temporary form at basic pH is fixed by its immersion in an aqueous solution containing Fe3+ ions. Shape recovery takes place in a controllable way by sequential steps that imply the increase of H<sup>+</sup> concentration in the aqueous media.

When it comes to N-donor ligands pyridine, imidazole and cyanide groups have been employed with redox active Cu2+ and nonactive Zn2+ ions to lock the temporary shape. For redox sensitive Cu2+-pyridine bonds (**Figure 5**), the reduction to Cu<sup>+</sup> *via* sodium metabisulphite was used as the external stimulus required to recover the original shape through a process that involved not only the cited shape memory behavior, but also changes in the color and mechanical properties of the material [41]. On the contrary, the polyacrylate chains with

**Figure 5.** Schematic representation of the SME in redox-sensitive hydrogels based on metal-coordination bonds between copper cations and pyridine groups.

imidazole side groups generated a SMH based on Zn2+/imidazole bonds whose shape can only be reversed by the addition of strong chelating agents such as EDTA [42]. In a closely related work, a UV-light triggered shape memory was described in a similar polymeric matrix. In this case, diphenyliodonium nitrate was incorporated which generates protons under UV light leading to the protonation of imidazole groups and consequent cleavage of coordination bonds [43]. Regarding cyanide containing materials, Liu et al. reported on dipole-dipole reinforced, acrylonitrile-based, ultra-high strength hydrogels that displays triple shape memory effect regulated by zinc ion concentration. Additional investigations by this group demonstrated that the temporary shape can be pre-programmed by surface micropatterning [12, 43].

cationic 3-(methacryloylamino)propyltrimethylammonium, anionic *p*-styrenesulfonate and neutral methacrylic acid monomers in a one-step process. Apart from the pH-dependent shape memory effect that can be repeated over 10 times, the hydrogel showed a spontaneous shape change after the first cycle. Therefore, the hydrogel prepared was proposed as a starting point for the design of new soft actuators that require successive actions. However, the preparation of the desired shape memory material in polyampholyte hydrogels is often challenging. As shown by previous works, different authors were forced to incorporate Fe3+ ions or to induce

Shape Memory Hydrogels Based on Noncovalent Interactions

http://dx.doi.org/10.5772/intechopen.78013

105

Although the field of shape memory hydrogels based on electrostatic assembly is basically limited to simple metal-ion containing systems, recent advances in self-healing hydrogels that incorporate another inorganic entities provide new ideas that could be promisingly exploited with the aim of pursuing shape-memory behavior. Indeed temporary ionic bonds are in the origin of (1) the rapid self-healing ability of mechanically robust hybrid PAA hydrogels that contain amino-derivatized nanometric polyhedral oligomeric silsesquioxanes (POSS) [50]; (2) the magnetic auto-repairing ability of a chitosan-based hydrogel loaded with magnetite

) nanoparticles that display coatings modified with carboxylic acid functionalities [51];

and (3) the combination of anionic polyoxometalate (POM) [EuW10O36]9− oxo-clusters with cationic triblock copolymers bearing guanidinium groups that result in hybrid hydrogels with

Triple-shape or multishape memory hydrogels can be designed by a combination of two or more noninterfering dynamic switches incorporated in hydrogel's network [53]. In spite of the great variety of supramolecular interactions described above, triple/multiple shape memory effect still represents a great challenge. This class of SSMH is capable to store two or more metastable shapes in addition to the original shape. In contrast to conventional shape memory polymers in which temporally switches are based on temperature changes, SSMHs can respond to different stimuli (pH, redox…) through sequential changes at room temperature [54]. This kind of hydrogels is until now less studied, and only few examples have been reported. Xiao et al. have demonstrated the triple-shape and multishape memory effect by using two reversible interactions based on dynamic covalent interactions and metal–ligand coordination bonds. The hydrogel was prepared by the polymerization of acrylamide monomer in the presence of chitosan and oxidized dextran. The temporary shape could be obtained by multiresponsive Schiff base-type bonds established between the amino groups of chitosan and the aldehyde groups of the oxidized dextran. In addition, other secondary temporary shape could be fixed with the chelating capability of the chitosan with several metal cations [53]. More complicated studies have been devoted to the hydrogels based on three switchers based on metal-ligand coordination, dynamic covalent bonds and coil-helix transaction. Each of these interactions could fix one temporary shape in the hydrogel. The first temporary shape was achieved by coordination of acrylic acid moieties to Fe3+ cations. A second temporary shape was fixed by the reaction between phenylboronic acid (PBA) and 1,2-diols forming ester

salt-dependent hydrophobic association in order to fix the temporary shape [18].

both tunable luminescent and self-healing capability [52].

**3. Multishape memory effect**

(Fe<sup>3</sup> O4

## **2.5. Electrostatic interactions**

Ionic temporary crosslink has been long used to induce self-healing behavior in covalently cross-linked hydrogels. Electrostatic forces between anionic functional groups and cationic metal cations can afford highly stretchable and tough self-healable hydrogels, as exemplified by photo-cross-linked polyacrylamide networks with Ca2+-alginate interactions [44]. Following this approach and combining it with covalent boronate ester dynamic bonds, a dual shape memory/self-healing PVA hydrogel was developed where the incorporations/ removal of Ca2+ ions was used to trigger the shape recovery process [45]. According to the authors, the temporary state can be fixed in 30 s, much faster than other shape memory hydrogels induced by metal ions, which need hours for that purpose. This is the case of acrylamide/ isoprenyl phosphonic acid copolymers cross-linked by PEG diacrylate where the presence of Fe3+ ions allows the shape memory to take place [46]. In both systems, the extraction of metal ions with EDTA chelating agent completely recovers the original shape. Additionally, the reduction of Fe3+ with erythorbic acid for the later example and the removal of Ca2+ ions upon immersion of the hydrogel in basic aqueous media for the former can be applied as alternative recovering stimuli. Among the alginate-based shape-memory materials, it is worth highlighting the superelastic hydrogel that incorporates flexible SiO<sup>2</sup> nanofibers and exhibits pressure-dependent conductivity. Trivalent Al3+ cations facilitate complete recovery from 80% strain in this ultrahigh water content hydrogel (99.8 wt%) [47].

The electrostatic approach can be applied in combination with not only dynamic covalent bonds, but also another additional temporary interactions such as hydrogen bonds as was demonstrated by Ca2+-triggered shape memory properties in PVDT-PAA (VDT = 2-vinyl-4,6-diamino-1,3,5-triazine) hydrogels synthesized *via* photo-polymerization [48]. The low cytotoxicity of the system encouraged the authors to evaluate biological aspects. It was proved that cells could adhere to the hydrogel surface, and afterward, they can be conveniently detached by simply adding calcium ions without influencing their viability. Thus, this dual strategy paves the way for the design of new multifunctional high strength hydrogels for biomedical applications.

Besides the addition of metal cations, charged groups can also be coexisting in zwitterionic copolymers. Classic examples include those in which anionic carboxylate or sulfonate monomers and cationic ammonium units are copolymerized with neutral comonomers. These hydrogels can show the shape memory behavior in the absence of any chemical cross-linker or addition of metal salts. Tong [49] have opted for synthesizing polyampholyte hydrogels by reacting cationic 3-(methacryloylamino)propyltrimethylammonium, anionic *p*-styrenesulfonate and neutral methacrylic acid monomers in a one-step process. Apart from the pH-dependent shape memory effect that can be repeated over 10 times, the hydrogel showed a spontaneous shape change after the first cycle. Therefore, the hydrogel prepared was proposed as a starting point for the design of new soft actuators that require successive actions. However, the preparation of the desired shape memory material in polyampholyte hydrogels is often challenging. As shown by previous works, different authors were forced to incorporate Fe3+ ions or to induce salt-dependent hydrophobic association in order to fix the temporary shape [18].

Although the field of shape memory hydrogels based on electrostatic assembly is basically limited to simple metal-ion containing systems, recent advances in self-healing hydrogels that incorporate another inorganic entities provide new ideas that could be promisingly exploited with the aim of pursuing shape-memory behavior. Indeed temporary ionic bonds are in the origin of (1) the rapid self-healing ability of mechanically robust hybrid PAA hydrogels that contain amino-derivatized nanometric polyhedral oligomeric silsesquioxanes (POSS) [50]; (2) the magnetic auto-repairing ability of a chitosan-based hydrogel loaded with magnetite (Fe<sup>3</sup> O4 ) nanoparticles that display coatings modified with carboxylic acid functionalities [51]; and (3) the combination of anionic polyoxometalate (POM) [EuW10O36]9− oxo-clusters with cationic triblock copolymers bearing guanidinium groups that result in hybrid hydrogels with both tunable luminescent and self-healing capability [52].

## **3. Multishape memory effect**

imidazole side groups generated a SMH based on Zn2+/imidazole bonds whose shape can only be reversed by the addition of strong chelating agents such as EDTA [42]. In a closely related work, a UV-light triggered shape memory was described in a similar polymeric matrix. In this case, diphenyliodonium nitrate was incorporated which generates protons under UV light leading to the protonation of imidazole groups and consequent cleavage of coordination bonds [43]. Regarding cyanide containing materials, Liu et al. reported on dipole-dipole reinforced, acrylonitrile-based, ultra-high strength hydrogels that displays triple shape memory effect regulated by zinc ion concentration. Additional investigations by this group demonstrated that the temporary shape can be pre-programmed by surface micropatterning [12, 43].

Ionic temporary crosslink has been long used to induce self-healing behavior in covalently cross-linked hydrogels. Electrostatic forces between anionic functional groups and cationic metal cations can afford highly stretchable and tough self-healable hydrogels, as exemplified by photo-cross-linked polyacrylamide networks with Ca2+-alginate interactions [44]. Following this approach and combining it with covalent boronate ester dynamic bonds, a dual shape memory/self-healing PVA hydrogel was developed where the incorporations/ removal of Ca2+ ions was used to trigger the shape recovery process [45]. According to the authors, the temporary state can be fixed in 30 s, much faster than other shape memory hydrogels induced by metal ions, which need hours for that purpose. This is the case of acrylamide/ isoprenyl phosphonic acid copolymers cross-linked by PEG diacrylate where the presence of Fe3+ ions allows the shape memory to take place [46]. In both systems, the extraction of metal ions with EDTA chelating agent completely recovers the original shape. Additionally, the reduction of Fe3+ with erythorbic acid for the later example and the removal of Ca2+ ions upon immersion of the hydrogel in basic aqueous media for the former can be applied as alternative recovering stimuli. Among the alginate-based shape-memory materials, it is worth

pressure-dependent conductivity. Trivalent Al3+ cations facilitate complete recovery from 80%

The electrostatic approach can be applied in combination with not only dynamic covalent bonds, but also another additional temporary interactions such as hydrogen bonds as was demonstrated by Ca2+-triggered shape memory properties in PVDT-PAA (VDT = 2-vinyl-4,6-diamino-1,3,5-triazine) hydrogels synthesized *via* photo-polymerization [48]. The low cytotoxicity of the system encouraged the authors to evaluate biological aspects. It was proved that cells could adhere to the hydrogel surface, and afterward, they can be conveniently detached by simply adding calcium ions without influencing their viability. Thus, this dual strategy paves the way for the design of new multifunctional high strength hydrogels for biomedical applications.

Besides the addition of metal cations, charged groups can also be coexisting in zwitterionic copolymers. Classic examples include those in which anionic carboxylate or sulfonate monomers and cationic ammonium units are copolymerized with neutral comonomers. These hydrogels can show the shape memory behavior in the absence of any chemical cross-linker or addition of metal salts. Tong [49] have opted for synthesizing polyampholyte hydrogels by reacting

nanofibers and exhibits

highlighting the superelastic hydrogel that incorporates flexible SiO<sup>2</sup>

strain in this ultrahigh water content hydrogel (99.8 wt%) [47].

**2.5. Electrostatic interactions**

104 Shape-Memory Materials

Triple-shape or multishape memory hydrogels can be designed by a combination of two or more noninterfering dynamic switches incorporated in hydrogel's network [53]. In spite of the great variety of supramolecular interactions described above, triple/multiple shape memory effect still represents a great challenge. This class of SSMH is capable to store two or more metastable shapes in addition to the original shape. In contrast to conventional shape memory polymers in which temporally switches are based on temperature changes, SSMHs can respond to different stimuli (pH, redox…) through sequential changes at room temperature [54]. This kind of hydrogels is until now less studied, and only few examples have been reported. Xiao et al. have demonstrated the triple-shape and multishape memory effect by using two reversible interactions based on dynamic covalent interactions and metal–ligand coordination bonds. The hydrogel was prepared by the polymerization of acrylamide monomer in the presence of chitosan and oxidized dextran. The temporary shape could be obtained by multiresponsive Schiff base-type bonds established between the amino groups of chitosan and the aldehyde groups of the oxidized dextran. In addition, other secondary temporary shape could be fixed with the chelating capability of the chitosan with several metal cations [53]. More complicated studies have been devoted to the hydrogels based on three switchers based on metal-ligand coordination, dynamic covalent bonds and coil-helix transaction. Each of these interactions could fix one temporary shape in the hydrogel. The first temporary shape was achieved by coordination of acrylic acid moieties to Fe3+ cations. A second temporary shape was fixed by the reaction between phenylboronic acid (PBA) and 1,2-diols forming ester bonds under basic pH (pH = 10). Finally, the third temporary shape was fixed by coil-helix transition of the agar structure that represents switch rarely used in the design of this kind of hydrogels [55]. A very similar approach was described by Le et al. where a triple-shape memory was based on PBA-diol bonds and the coordination interactions between alginate and calcium cations [56].

**References**

2017.05.020

accounts.6b00584

DOI: 10.1002/adma.201601613

120. DOI: 10.1016/j.progpolymsci.2015.04.001

2012;**7**:1720-1763. DOI: 10.1016/j.progpolymsci.2012.06.001

Chemical Society Reviews. 2013;**2**:7244. DOI: 10.1039/c3cs35489j

Communications. 2012;**33**:225-231. DOI: 10.1002/marc.201100683

Materials Chemistry. 2007;**17**:1543. DOI: 10.1039/b615954k

**52**:10609-10612. DOI: 10.1039/C6CC03587F

13075. DOI: 10.1021/am404087q

[1] Langer R, Peppas NA. Advances in biomaterials, drug delivery, and bionanotechnology.

Shape Memory Hydrogels Based on Noncovalent Interactions

http://dx.doi.org/10.5772/intechopen.78013

107

[2] Gupta P, Vermani K, Garg S. Hydrogels: From controlled release to pH-responsive drug delivery. Drug Discovery Today. 2002;**7**:569-579. DOI: 10.1016/S1359-6446(02)02255-9 [3] Richter AA, Paschew G, Klatt S, Lienig J, Arndt KF, HJP A. Review on hydrogel-based pH sensors and microsensors. Sensors. 2008;**8**:561-581. DOI: 10.3390/s8010561

[4] Gyarmati B, Szilágyi BA, Szilágyi A.Reversible interactions in self-healing and shape memory hydrogels. European Polymer Journal. 2017;**93**:642-669. DOI: 10.1016/j.eurpolymj.

[5] Taylor DL. in het Panhuis M. Self-Healing Hydrogels. Adv. Maternité. 2016;**8**:9060-9093.

[6] Löwenberg C, Balk M, Wischke C, Behl M, Lendlein A. Shape-memory hydrogels: Evolution of structural principles to enable shape switching of hydrophilic polymer networks. Accounts of Chemical Research. 2017;**50**:723-732. DOI: 10.1021/acs.

[7] Zhao Q, Qi HJ, Xie T. Recent progress in shape memory polymer: New behavior, enabling materials, and mechanistic understanding. Progress in Polymer Science. 2015;**49-50**:79-

[8] Hu J, Zhu Y, Huang H, Lu J. Recent advances in shape-memory polymers: Structure, mechanism, functionality, modeling and applications. Progress in Polymer Science.

[9] Li G, Zhang H, Fortin D, Xia H, Zhao Y. Poly(vinyl alcohol)–poly(ethylene glycol) double-network hydrogel: A general approach to shape memory and self-healing func-

[10] Habault D, Zhang H, Zhao Y. Light-triggered self-healing and shape-memory polymers.

[11] Liu C, Qin H, Mather PT. Review of progress in shape-memory polymers. Journal of

[12] Han Y, Bai T, Liu Y, Zhai X, Liu W. Zinc ion uniquely induced triple shape memory effect of dipole-dipole reinforced ultra-high strength hydrogels. Macromolecular Rapid

[13] Xiao YY, Gong XL, Kang Y, Jiang ZC, Zhang S, Li BJ. Light-, pH- and thermal-responsive hydrogels with the triple-shape memory effect. Chemical Communications. 2016;

[14] Zhang H, Zhao Y. Polymers with dual light-triggered functions of shape memory and healing using gold nanoparticles. ACS Applied Materials & Interfaces. 2013;**5**:13069-

tionalities. Langmuir. 2015;**31**:11709-11716. DOI: 10.1021/acs.langmuir.5b03474

AICHE Journal. 2003;**49**:2990-3006. DOI: 10.1002/aic.690491202

## **4. Conclusion**

In summary, highly promising advances have been made in the development of supramolecular shape memory hydrogels, and a plethora of new hydrogels will be synthesized in the following years due to the versatility of the supramolecular interactions. In addition, the self-healable capability and their adequate biocompatible properties added great capability of adaptation to different requirements.

## **Acknowledgements**

This work has been funded by UPV/EHU (grant PG17/37, IT1082-16, IT718-13), MINECO (MAT2017-89553-P). B.A. thanks the Vice-rectorate for Research of UPV/EHU for a postdoctoral fellowship within the program "Convocatorias de Ayudas para la Especialización de Personal Investigador."

## **Conflict of Interest**

The authors declare no conflict of interest.

## **Author details**

Leire Ruiz-Rubio1,3\*, Leyre Pérez-Álvarez1,3, Beñat Artetxe<sup>2</sup> , Juan M. Gutiérrez-Zorrilla2,3 and José Luis Vilas1,3

\*Address all correspondence to: leire.ruiz@ehu.eus

1 Macromolecular Chemistry Group (LABQUIMAC), Department of Physical Chemistry, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Bilbao, Spain

2 Department of Inorganic Chemistry, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Bilbao, Spain

3 BCMaterials, Basque Center for Materials, Applications and Nanostructures, UPV/EHU Science Park, Leioa, Spain

## **References**

bonds under basic pH (pH = 10). Finally, the third temporary shape was fixed by coil-helix transition of the agar structure that represents switch rarely used in the design of this kind of hydrogels [55]. A very similar approach was described by Le et al. where a triple-shape memory was based on PBA-diol bonds and the coordination interactions between alginate

In summary, highly promising advances have been made in the development of supramolecular shape memory hydrogels, and a plethora of new hydrogels will be synthesized in the following years due to the versatility of the supramolecular interactions. In addition, the self-healable capability and their adequate biocompatible properties added great capability of

This work has been funded by UPV/EHU (grant PG17/37, IT1082-16, IT718-13), MINECO (MAT2017-89553-P). B.A. thanks the Vice-rectorate for Research of UPV/EHU for a postdoctoral fellowship within the program "Convocatorias de Ayudas para la Especialización de

1 Macromolecular Chemistry Group (LABQUIMAC), Department of Physical Chemistry, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Bilbao,

2 Department of Inorganic Chemistry, Faculty of Science and Technology, University of the

3 BCMaterials, Basque Center for Materials, Applications and Nanostructures, UPV/EHU

, Juan M. Gutiérrez-Zorrilla2,3 and

and calcium cations [56].

adaptation to different requirements.

**Acknowledgements**

Personal Investigador."

**Conflict of Interest**

**Author details**

José Luis Vilas1,3

Spain

The authors declare no conflict of interest.

Leire Ruiz-Rubio1,3\*, Leyre Pérez-Álvarez1,3, Beñat Artetxe<sup>2</sup>

\*Address all correspondence to: leire.ruiz@ehu.eus

Basque Country UPV/EHU, Bilbao, Spain

Science Park, Leioa, Spain

**4. Conclusion**

106 Shape-Memory Materials


[15] Ratna D, Karger-Kocsis J. Recent advances in shape memory polymers and composites: A review. Journal of Materials Science. 2008;**43**:254-269. DOI: 10.1007/s10853-007-2176-7

[28] Hu Y, Lu CH, Guo W, Aleman-Garcia MA, Ren J, Willner I. A shape memory acrylamide/ DNA hydrogel exhibiting switchable dual pH-responsiveness. Advanced Functional

Shape Memory Hydrogels Based on Noncovalent Interactions

http://dx.doi.org/10.5772/intechopen.78013

109

[29] Hu Y, Guo W, Kahn JS, Aleman-Garcia MA, Willner I. A shape-memory DNA-based hydrogel exhibiting two internal memories. Angewandte Chemie International Edition.

[30] Lu CH, Guo W, Hu Y, Qi XJ, Willner I. Multitriggered shape-memory acrylamide–DNA hydrogels. Journal of the American Chemical Society. 2015;**137**:15723-15731. DOI: 10.1021/

[31] Strandman S, Zhu XX. Self-healing supramolecular hydrogels based on reversible physi-

[32] Webber MJ, Langer R. Drug delivery by supramolecular design. Chemical Society

[33] Sliwa W, Girek T. CD-based rotaxanes and polyrotaxanes as representative supramolecules. In: Sliwa W, Girek T, editors. Cyclodextrins. Weinhenim: Wiley-VCH Verlag;

[34] Feng W, Zhou W, Dai Z, Yasin A, Yang H. Tough polypseudorotaxane supramolecular hydrogels with dual-responsive shape memory properties. Journal of Materials

[35] Cai T, Huo S, Wang T, Sun W, Tong Z. Self-healable tough supramolecular hydrogels crosslinked by poly-cyclodextrin through host-guest interaction. Carbohydrate

[36] Dong ZQ, Cao YY, Yuan QJ, Wang YF, Li JH, Li BJ, Zhang S. Redox- and glucose-induced shape-memory polymers. Macromolecular Rapid Communications. 2013;**34**:867-872.

[37] Han XJ, Dong ZQ, Fan MM, Liu Y, Li JH, Wang YF, Yuan QJ, Li BJ, Zhang S. pH-induced shape-memory polymers. Macromolecular Rapid Communications. 2012;**33**:1055-1060.

[38] Zhang T, Silverstein MS. Doubly-crosslinked, emulsion-templated hydrogels through reversible metal coordination. Polymer. 2017;**126**:386-394. DOI: 10.1016/j.polymer.2017.

[39] Zheng SY, Ding H, Qian J, Yin J, Wu ZL, Song Y, Zheng Q. Metal-coordination complexes mediated physical hydrogels with high toughness, stick–slip tearing behavior, and good processability. Macromolecules. 2016;**49**:9637-9646. DOI: 10.1021/acs.macromol.6b02150

[40] Le X, Zhang Y, Lu W, Wang L, Zheng J, Ali I, Zhang J, Huang Y, Serpe MJ, Yang X, Fan X, Chen T. A novel anisotropic hydrogel with integrated self-deformation and controllable shape memory effect. Macromolecular Rapid Communications. 2018:1800019. DOI:

[41] Harris RD, Auletta JT, Motlagh SAM, Lawless MJ, Perri NM, Saxena S, Weiland LM, Waldeck DH, Clark WW, Meyer TY. Chemical and electrochemical manipulation of

Materials. 2015;**25**:6867-6874. DOI: 10.1002/adfm.201503134

cal interactions. Gels. 2016;**2**:16. DOI: 10.3390/gels2020016

Reviews. 2017;**46**:6600-6620. DOI: 10.1039/C7CS00391A

Chemistry B. 2016;**4**:1924-1931. DOI: 10.1039/C5TB02737C

Polymers. 2018;**193**:54-61. DOI: 10.1016/j.carbpol.2018.03.039

2017. pp. 9-50. DOI: 10.1002/9783527695294.ch1

DOI: 10.1002/marc.201300084

DOI: 10.1002/marc.201200153

10.1002/marc.201800019

07.044

2016;**55**:4210-4214. DOI: 10.1002/anie.201511201

jacs.5b06510


[28] Hu Y, Lu CH, Guo W, Aleman-Garcia MA, Ren J, Willner I. A shape memory acrylamide/ DNA hydrogel exhibiting switchable dual pH-responsiveness. Advanced Functional Materials. 2015;**25**:6867-6874. DOI: 10.1002/adfm.201503134

[15] Ratna D, Karger-Kocsis J. Recent advances in shape memory polymers and composites: A review. Journal of Materials Science. 2008;**43**:254-269. DOI: 10.1007/s10853-007-2176-7

[16] Bilici C, Can V, Nöchel U, Behl M, Lendlein A, Okay O. Melt-processable shape-memory hydrogels with self-healing ability of high mechanical strength. Macromolecules. 2016;

[17] Miyamae K, Nakahata M, Takashima Y, Harada A. Self-healing, expansion-contraction, and shape-memory properties of a preorganized supramolecular hydrogel through host-guest interactions. Angewandte Chemie International Edition. 2015;**54**:8984-8987.

[18] Fan Y, Zhou W, Yasin A, Li H, Yang H. Dual-responsive shape memory hydrogels with novel thermoplasticity based on a hydrophobically modified polyampholyte. Soft

[19] Li Z, Lu W, Ngai T, Le X, Zheng J, Zhao N, Huang Y, Wen X, Zhang J, Chen T. Musselinspired multifunctional supramolecular hydrogels with self-healing, shape memory and adhesive properties. Polymer Chemistry. 2016;**7**:5343-5346. DOI: 10.1039/C6PY01112H

[20] Nieuwenhuizen MML, TFA DG, Der Bruggen RLJ V, Paulusse JMJ, Appel WPJ, Smulders MMJ, Sijbesma RP, Meijer EW. Self-assembly of ureido-pyrimidinone dimers into onedimensional stacks by lateral hydrogen bonding. Chemistry – A European Journal.

[21] Chen H, Li Y, Tao G, Wang L, Zhou S. Thermo- and water-induced shape memory poly(vinyl alcohol) supramolecular networks crosslinked by self-complementary quadruple hydrogen bonding. Polymer Chemistry. 2016;**7**:6637-6644. DOI: 10.1039/C6PY01302C

[22] Zhang G, Chen Y, Deng Y, Ngai T, Wang C.Dynamic supramolecular hydrogels: Regulating Hydrogel properties through self-complementary quadruple hydrogen bonds and thermo-switch. ACS Macro Letters. 2017;**6**:641-646. DOI: 10.1021/acsmacrolett.7b00275

[23] Xu B, Zhang Y, Liu W. Hydrogen-bonding toughened hydrogels and emerging CO<sup>2</sup> -responsive shape memory effect. Macromolecular Rapid Communications. 2015;

[24] Chen YN, Peng L, Liu T, Wang Y, Shi S, Wang H. Poly(vinyl alcohol)-tannic acid hydrogels with excellent mechanical properties and shape memory behaviors. ACS Applied

[25] Skrzeszewska PJ, Jong LN, de Wolf FA, Cohen Stuart MA, van der Gucht J. Shape-memory effects in biopolymer networks with collagen-like transient nodes. Biomacromolecules

[26] Huang J, Zhao L, Wang T, Sun W, Tong Z. NIR-triggered rapid shape memory PAM–GO– gelatin hydrogels with high mechanical strength. ACS Applied Materials & Interfaces.

[27] Guo W, Lu CH, Orbach R, Wang F, Qi XJ, Cecconello A, Seliktar D, Willner I. pH-stimulated DNA hydrogels exhibiting shape-memory properties. Advanced Materials. 2015;**27**:73-78.

Materials & Interfaces. 2016;**8**:27199-27206. DOI: 10.1021/acsami.6b08374

**49**:7442-7449. DOI: 10.1021/acs.macromol.6b01539

Matter. 2015;**11**:4218-4225. DOI: 10.1039/C5SM00168D

2010;**16**:1601-1612. DOI: 10.1002/chem.200902107

**36**:1585-1591. DOI: 10.1002/marc.201500256

2011;**12**:2285-2292. DOI: 10.1021/bm2003626

DOI: 10.1002/adma.201403702

2016;**8**:12384-12392. DOI: 10.1021/acsami.6b00867

DOI: 10.1002/anie.201502957

108 Shape-Memory Materials


mechanical properties in stimuli-responsive copper-cross-linked hydrogels. ACS Macro Letters. 2013;**2**:1095-1099. DOI: 10.1021/mz4004997


mechanical properties in stimuli-responsive copper-cross-linked hydrogels. ACS Macro

[42] Nan W, Wang W, Gao H, Liu W. Fabrication of a shape memory hydrogel based on imidazole–zinc ion coordination for potential cell-encapsulating tubular scaffold application.

[43] Feng W, Zhou W, Zhang S, Fan Y, Yasin A, Yang H. UV-controlled shape memory hydrogels triggered by photoacid generator. RSC Advances. 2015;**5**:81784-81789. DOI: 10.1039/

[44] Sun JY, Zhao X, Illeperuma WRK, Chaudhuri O, Oh KH, Mooney DJ, Vlassak JJ, Suo Z. Highly stretchable and tough hydrogels. Nature. 2012;**489**:133-136. DOI: 10.1038/nature

[45] Meng H, Xiao P, Gu J, Wen X, Xu J, Zhao C, Zhang J, Chen T. Self-healable macro−/ microscopic shape memory hydrogels based on supramolecular interactions. Chemical

[46] Yasin A, Li H, Lu Z, ur Rehman S, Siddiq M, Yang H. A shape memory hydrogel induced by the interactions between metal ions and phosphate. Soft Matter. 2014;**10**:972-977.

[47] Si Y, Wang L, Wang X, Tang N, Yu J, Ding B. Ultrahigh-water-content, superelastic, and shape-memory nanofiber-assembled hydrogels exhibiting pressure-responsive conduc-

[48] Ren Z, Zhang Y, Li Y, Xu B, Liu W. Hydrogen bonded and ionically crosslinked high strength hydrogels exhibiting Ca2+ −triggered shape memory properties and volume shrinkage for cell detachment. Journal of Materials Chemistry B. 2015;**3**:6347-6354. DOI:

[49] Zhang Y, Liao J, Wang T, Sun W, Tong Z. Polyampholyte hydrogels with pH modulated shape memory and spontaneous actuation. Advanced Functional Materials. 2018:

[50] Pu W, Jiang F, Chen P, Wei B. A POSS based hydrogel with mechanical robustness, cohesiveness and a rapid self-healing ability by electrostatic interaction. Soft Matter.

[51] Zhang Y, Yang B, Zhang X, Xu L, Tao L, Li S, Wei Y. A magnetic self-healing hydrogel.

[52] Wei H, Du S, Liu Y, Zhao H, Chen C, Li Z, Lin J, Zhang Y, Zhang J, Wan X. Tunable, luminescent, and self-healing hybrid hydrogels of polyoxometalates and triblock copolymers based on electrostatic assembly. Chemical Communications. 2014;**50**:1447-1450.

Chemical Communications. 2012;**48**:9305. DOI: 10.1039/c2cc34745h

tivity. Advanced Materials. 2017;**29**:1700339. DOI: 10.1002/adma.201700339

Communications. 2014;**50**:12277-12280. DOI: 10.1039/C4CC04760E

Letters. 2013;**2**:1095-1099. DOI: 10.1021/mz4004997

Soft Matter. 2013;**9**:132-137. DOI: 10.1039/C2SM26918J

C5RA14421C

DOI: 10.1039/C3SM52666F

10.1039/C5TB00781J

DOI: 10.1039/C3CC48732F

1707245. DOI: 10.1002/adfm.201707245

2017;**13**:5645-5648. DOI: 10.1039/C7SM01492A

11409

110 Shape-Memory Materials

## *Edited by Alicia Esther Ares*

Shape-memory materials are materials that react under variations of electric or magnetic fields, physical or chemical changes, and that when returning to the initial conditions recover their original form, capable of repeating this process an infinite number of times without deteriorating.

The characteristics, fabrication techniques, and thermomechanical treatment of various shape-memory materials are described in detail in this book. The book describes several principles and applications.

Published in London, UK © 2018 IntechOpen © nespix / iStock

Shape-Memory Materials

Shape-Memory Materials

*Edited by Alicia Esther Ares*