**1. Introduction**

120 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

editor. Cutting Edge Robotics 2010. Rijeka: InTech. pp. 333-350.

assistive devices actuated by smart materials.

joint passive moment. J Biomech. 29: 443-450.

and Evaluation. J Med Biol Eng 28: 79-86.

Actuators. J Mater Eng Perform 18: 691-695.

Psychiatry 59: 271-279.

and essential performance.

practice.

127.

[50] Patent Number: US 6379393 B1. Prosthetic, orthotic, and other rehabilitative robotic

[51] Jayatilake D, Gruebler A, Suzuki K (2010) Robot Assisted Smile Recovery. In: Kordic V,

[52] Esteki A, Mansour JM (1996) An experimentally based nonlinear viscoelastic model of

[53] Given JD, Dewald JPA, Rymer WZ (1995) Joint dependent passive stiffness in paretic and contralateral limbs of spastic patients with hemiparetic stroke. J Neurol Neurosurg

[54] Lin CCK, Ju MS, Chen SM, Pan BW (2008) A Specialized Robot for Ankle Rehabilitation

[55] IEC 60601-1. Medical electrical equipment - Part 1: General requirements for basic safety

[57] ISO 14155. Clinical investigation of medical devices for human subjects - Good clinical

[58] Fumagalli L, Butera F, Coda A (2009) SmartFlex® NiTi Wires for Shape Memory

[59] Liu SH, Huang TS, Yen JY (2010) Tracking Control of Shape-Memory-Alloy Actuators Based on Self-Sensing Feedback and Inverse Hysteresis Compensation. Sensors 10: 112-

[56] ISO 14971. Medical devices - Application of risk management to medical devices.

A one-dimensional phenomenological approach to simulate both the mechanical and functional properties in shape memory alloys (SMAs) is described in the following sections. In fact, shape-memory alloys exhibit unique mechanical and functional features, due to reversible transformations in crystal structure. In particular, on the macroscopic scale, SMAs are able to remember a geometrical shape and can return to that shape by activating the phase transition mechanisms. Many kinds of SMAs have been exploited in the last decades, such as the copper-zinc-aluminum (ZnCuAl), copper-aluminum-nickel (CuAlNi), nickel-manganese-gallium (NiMnGa), nickel-titanium (NiTi), and other ones made by alloying zinc, copper, gold, iron, etc. Among these alloys the near equiatomic NiTi binary system shows the most exploitable characteristics due to the high stress and strain recovery capabilities associated with their functional properties, namely pseudoelastic effect (PE) and shape memory effect (SME). These properties are due to a reversible solid state phase transformation between a parent phase (austenite) and a product phase (martensite), the so called thermoelastic martensitic transformation (TMT), that can be activated either by temperature (Thermally Induced Martensite, TIM), or by applied stress (Stress Induced Martensite, SIM) [1]. Due to these features NiTi alloys are currently used in an increasing number of applications in many fields of engineering [2], for the realization of smart sensors and actuators, joining devices, hydraulic and pneumatic valves, release/separation systems, consumer applications and commercial gadgets. However, thanks to their good mechanical properties and biocompatibility the most important applications of NiTi alloys are in the field of medicine, where pseudoelasticity is mainly exploited for the realization of several components, such as cardiovascular stent, embolic protection filters, orthopedic components, orthodontic wires, micro surgical and endoscopic devices. As a direct consequence of their interesting features NiTi alloys have attracted the interest of scientific and engineering community in the last years. However, despite the increasing interest and the efforts of many researchers to better understand these unusual mechanisms, the use of NiTi alloys is currently

©2012 Maletta and Furgiuele, licensee InTech. This is an open access chapter 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. © 2012 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.

#### 2 Will-be-set-by-IN-TECH 122 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

limited to high-value applications (i.e. medical devices, MEMS, etc.), due to the high cost of the raw material as well as to the complex component manufacturing; in fact, an accurate control of the processing parameters must be carried out as the functional and mechanical properties of NiTi alloys are significantly affected by the thermo-mechanical loading history experienced during manufacturing [3–8]. On the other hand, the design of complex shaped NiTi-based components needs an accurate knowledge of the mechanical and functional response of the material, as well as how this evolves during subsequent thermo-mechanical processes. Within this context the use of numerical modeling techniques, to simulate both mechanical and functional behavior of SMAs, is of major concern and, consequently, many studies have been focused on this topic in the last few years [9, 10], with the aim to model the non-linear hysteretic behavior that describes the phase transformation, and the related functional properties. Some of these models are based on microscopic and mesoscopic approaches [10], where the thermo-mechanical behavior is modeled starting from molecular level and lattice level, respectively; other models are based on macroscopic approaches, where only phenomenological features of the SMAs are used [11–24]. In this field, some authors proposed one-dimensional models based on an assumed polynomial-free energy potential [11, 12] while other models are based on an assumed phase transformation kinetic and consider simple mathematical functions to describe the phase transformation behavior of the material [13–15]. These models are probably the most popular in the literature due to their phenomenological approaches, which allow easy developments without considering the underlying physics of the transformation kinetic. Furthermore, other models are based on the elastoplasticity theory [16–22] which are capable of describing the functional behavior of the material using plasticity concepts. Finally, some researchers used the Galerkin method to describe thermo-mechanical behaviors of shape memory alloys [23, 24]. More recently, a 1-D phenomenological approach to simulate both the shape memory effect [27–29] and pseudoelastic effect [30] in NiTi-based shape memory alloys has been developed and it is described in the following sections. In particular, the temperature-strain and stress-strain hysteretic behavior of SMAs, associated with the thermally induced and stress-induced phase transition mechanisms, are modeled from a phenomenological point of view, *i*.*e*. without considering the underlying physics of the problem, by using Prandtl-Ishlinksii hysteresis operators [25, 26]. The main features of this approach is a simple implementation together with a good accuracy and efficiency in predicting the stress-strain hysteretic behavior of 1D components. Unfortunately, the one dimensional nature of the proposed model, represents one of the major drawback with respect to some of the pre-existing phenomenological models, which are based on more thermodynamically consistent frameworks and, consequently, are able to capture several behaviors of NiTi alloys, such as detailed stress-strain distribution in 2D and 3D components. However, the high computational efficiency of the proposed model allows its use for real time simulation and control o 1D SMA components. The parameters of the phenomenological model are identified by simple and efficient numerical procedures, starting from a set of experimentally measured hysteresis loops. The identification procedures have been developed in the commercial software package *MatlabTM*, while the computed parameters are used in *SimulinkTM* models, which are able to simulate the whole path dependent hysteretic behavior of the SMAs, *i*.*e*. for generic complete and incomplete stress-induced and/or thermally induced phase transition mechanisms. The models are also able to capture the hysteresis modifications due to complex loading conditions, *i*.*e*. they are able to predict the change of the transformation stresses and temperatures according to the Clausius-Clapeyron relation [1]. The unique thermo-mechanical features of SMAs are firstly illustrated in the following section 2, while the numerical approach is described in section 3 together with some case studies, involving both shape memory and pseudoelasticity, and the results show good accuracy and small computational time.
