**2. Polyurethane foam as an energy absorbing material**

2 Will-be-set-by-IN-TECH

Polyurethane foam is nowadays being widely used in many energy absorption engineering applications such as cushioning and packaging [4, 15, 50]. Its use in automotive industry as an energy absorbing material in passive safety mechanisms goes beyond the protection functionality since it also provides more comfort, insulation and sound absorption. Thus, the role of this class of materials in vehicles is of special interest from both the consumer and the

On a microscopical level, most cellular materials, including polyurethane foams, have the ability to absorb energy while deforming due to the mechanics of cell crushing. In the process of absorbing impact energy, cell walls deform plastically and get damaged (e.g. fractured) [7,

Vehicle-to-vehicle side-impacts and vehicle rollover are presently among the most common types of car accidents and collisions. Additionally, these are also frequently the most serious accidents in terms of occupant injuries [6, 8, 39, 48]. Among these, frontal and side impact are the most severe. As a consequence, quite a large effort has been widely focused in improving passive and active safety mechanisms for frontal impact situations for the last decades. However, more recently, the number of serious injuries resulting from side-impacts has brought the attention of many researchers to the importance of developing similar or adapted mechanisms for such collisions [12, 33, 53]. In this type of collisions, the risk and/or the severity of the resulting injuries is frequently a direct consequence of the contact between the occupants and the lateral structure of the vehicle, given the reduced space between the occupant and the door [21]. Pelvic and chest areas have been reported by many authors as the

In the late 1990s Morris *et al.* [37] observed, through a series of numerical simulations of side-impact collisions, that the space available between the structure of the vehicle and the passengers is one of the most important parameters with direct influence on the levels of occupant's injuries. This statement was also supported by many other researches, as can be seen, for example, from the works of Tencer *et al.* [49] and Schiff *et al.* [44]. Morris *et al.* state that the space available not only has influence on the impact velocity but also on the point of the velocity profile at which the door initiates contact with the occupant. These authors also evaluated the benefits of the use of paddings of different sizes in the door interior and of lateral airbags. Lim *et al.* [26] also studied, numerically, the inclusion of padding material for protection of the occupant pelvic area and concluded that it significantly reduced the severity of the resulting injuries. Additionally, Majumder *et al.* [29] studied the dynamic response of the pelvis and established fracture limits in side-impact collisions. These authors supported their conclusions with the results from numerical simulations using finite element modelling software. One of the most important conclusion these researchers derived from their work was that with a more appropriate design of the lateral door and the inclusion of padding material on the level of the pelvic area, the risk and/or severity of occupants' injury could be

Based on the previous considerations, the authors propose the use of cellular materials, among which polyurethane foams, within an energy absorbing system specifically designed in such a way as to significantly improve passive safety on the event of side-impacts. This system

the two areas most affected in this type of car-to-car collision [29, 43, 44].

manufacturer points of view.

significantly reduced.

18].

The behaviour of three polymer based structural foams under compressive impact loading polypropylene, polyamide and rigid polyurethane foam — has been investigated by Avalle *et al.* [4]. As a conclusion, these materials are indicated as players of a very important role in passive safety systems. These authors obtained stress-strain curves in both static and impact loading (dynamic) conditions for the materials examined for different densities at room temperature. They analysed in detail, using energy-absorption and efficiency diagrams, the energy absorption characteristics of each material. Among the materials tested, these authors observed that polyurethane foam is the less sensitive to strain-rate and the one that presents the longest intermediate plateau stage. These facts distinguish this material from the remaining foams studied. The authors also concluded that the rigid polyurethane foam exhibited one of the highest efficiency levels, however, it lost its integrity during compression.

The energy absorption behaviour properties of polyurethane foam were also investigated by Anindya and Shivakumar [2]. The authors evaluated the energy absorption attributes of polyurethane foam in various forms — flexible high resilience, flexible viscoelastic and semi-rigid — as a function of the overall foam density, based on the load-displacement behaviour of the material under compressive loads.

Taher *et al.* [47] investigated the use of polyurethane foam with a density of 47 kg/m<sup>3</sup> as a core filler of a composite keel beam as a way of preventing global buckling and improving crashworthiness performance in aeroplanes and helicopters. The results obtained by these authors revealed that the energy absorbing mechanism can meet the requirements for the purpose desired together with substantial savings.

Likewise, the behaviour of polyurethane foam filled thin-wall structures was investigated by Ghamarian *et al.* [13] in terms of crashworthiness improvement for the aerospace industry. The quasi-static crushing behaviour and efficiency of empty and foam-filled structures was investigated experimental and numerically and the efficiency and the authors were able to demonstrate that the filled tubes presented higher energy absorption capabilities than that of the combined effect of the empty structured and the foam.

Furthermore, applications of polyurethane foam in explosive blast and ballistic energy absorption applications have also been subject of investigation [51, 52], indicating that this material may be a valuable part of protection systems against both generic types of threats.

Later, Shim *et al.* [45] investigated the two-dimensional behaviour of rigid polyurethane foam under low velocity impact loadings in terms of both the deceleration of the impactor and the overall amount of energy dissipated. These authors also proposed suitable stress-strain relations as well as failure patterns, failure criteria and equations of motion for this cellular material.

The foam used by Shim *et al.* [45] was obtained by blending — Daltofoam and Suprasec — in the presence of a blowing agent, producing a final product with a density of 25.6 kg/m3. Alike typical cellular materials the uniaxial compressive behaviour of this material can be described, in terms of stress-strain, by three distinct stages [14]. The first stage — the elastic deformation stage — is followed by a plastic constant stress stage (also known as "plateau" region) where most of the energy absorption occurs. Finally, the material exhibits densification. The elastic part of the behaviour of these materials is mostly due to the axial compressive resistance of the cell walls. The plateau region is mainly related to the bending, crushing and eventually fracture, of the cell walls. The material starts to densify when all the cells are crushed and the behaviour approaches the behaviour of a monolithic material [19, 42, 54].

The type of polyurethane foam investigated by Shim *et al.* [45] is adopted for the scope of this study and its stress-strain curve is represented on Figure 1, where the three stages are clearly evident. As the overall behaviour of this material can be divided in three distinct stages, its stress-strain constitutive modelling can be defined by the following set of equations:

$$\sigma = \begin{cases} \mathsf{E}\varepsilon & \text{if } \quad \varepsilon \in [0, \varepsilon\_{\mathrm{Y}}] \quad \text{(elastic behavior)} \\\\ \mathsf{E}\varepsilon\_{\mathrm{Y}} & \text{if } \quad \varepsilon \in [\varepsilon\_{\mathrm{Y}}, \varepsilon\_{\mathrm{d}}] \quad \text{(plastic behavior, plateau)} \\\\ \mathsf{E}\varepsilon\_{\mathrm{Y}} \exp\frac{a(\varepsilon - \varepsilon\_{\mathrm{d}})}{(\varepsilon\_{\mathrm{l}} - \varepsilon)^{b}} & \text{if } \quad \varepsilon \in [\varepsilon\_{\mathrm{d}}, \varepsilon\_{\mathrm{l}}] \quad \text{(densification)} \end{cases} \tag{1}$$

**Figure 1.** Stress-strain compressive behaviour of rigid polyurethane foam as obtained by [45].

were analysed in terms of acceleration peak and energy absorption.

*<sup>a</sup>* [11]; *<sup>b</sup>* [23, 45]; *<sup>c</sup>* [3];

comparison purposes.

*<sup>d</sup>*[10, 34].

elastic modulus, yield strength and Poisson coefficient of the base material, accordingly. The four materials share great energy absorption capabilities and are used in impact dissipation applications. For this purpose the materials were tested numerically, using a Finite Element Method simulation software, LS-Dyna™ [1], under impact loading in the same conditions and

On the Use of Polyurethane Foam Paddings to Improve Passive Safety in Crashworthiness Applications 341

**Mechanical Properties** *ρ*<sup>∗</sup> [kg/m3] *E*<sup>∗</sup> [MPa] *E* [MPa] *σ*<sup>y</sup> [MPa] *ν* Polyurethane Foam <sup>a</sup> 25.6 2.78 1600 127 0.44 Micro-agglomerated Cork <sup>b</sup> 293 15 9000 1 0.30 IMPAXX™ 33.661 16.322 3400 80 0.40 Aluminium Foam <sup>c</sup> 470 117 69000 241 0.285

**Table 1.** Mechanical properties of the polyurethane foam and of other cellular materials used for

Paulino and Teixeira-Dias[40] proposed a quantitative procedure that allows a padding or protection system designer to determine the crashworthiness efficiency and performance of specific cellular materials. This procedure assumes that the best method to assess the material

where *E* is the material elastic modulus (considered to be *E* = 2.78 MPa), *ε*<sup>y</sup> is the compressive yield strain (*ε*<sup>y</sup> = 0.05), *ε*<sup>d</sup> is the densification strain (*ε*<sup>d</sup> = 0.8), *ε*<sup>l</sup> is the maximum compressive strain (*ε*<sup>l</sup> = 0.95) and *a* and *b* are constants which define the shape of the stress-strain curve in the densification regime.

#### **3. Crashworthiness efficiency of polyurethane foam**

In previous investigations the authors used a Finite Element Analysis (FEA) approach to study the behaviour of four distinct cellular materials under impact loading in order to evaluate their relative efficiency in terms of crashworthiness applications [40]. The materials tested within these studies were two polymeric foams: polyurethane foam and IMPAXX™ ; a metallic foam: aluminium foam; and a natural cellular material: micro-agglomerated cork. The most relevant mechanical properties of these materials are listed on Table 1, where *ρ*∗ and *E*∗ are the density and elastic modulus of the cellular material, respectively, and *E*, *σ*y and *ν* are the

**Figure 1.** Stress-strain compressive behaviour of rigid polyurethane foam as obtained by [45].

elastic modulus, yield strength and Poisson coefficient of the base material, accordingly. The four materials share great energy absorption capabilities and are used in impact dissipation applications. For this purpose the materials were tested numerically, using a Finite Element Method simulation software, LS-Dyna™ [1], under impact loading in the same conditions and were analysed in terms of acceleration peak and energy absorption.


*<sup>a</sup>* [11]; *<sup>b</sup>* [23, 45]; *<sup>c</sup>* [3];

*<sup>d</sup>*[10, 34].

4 Will-be-set-by-IN-TECH

Furthermore, applications of polyurethane foam in explosive blast and ballistic energy absorption applications have also been subject of investigation [51, 52], indicating that this material may be a valuable part of protection systems against both generic types of threats. Later, Shim *et al.* [45] investigated the two-dimensional behaviour of rigid polyurethane foam under low velocity impact loadings in terms of both the deceleration of the impactor and the overall amount of energy dissipated. These authors also proposed suitable stress-strain relations as well as failure patterns, failure criteria and equations of motion for this cellular

The foam used by Shim *et al.* [45] was obtained by blending — Daltofoam and Suprasec — in the presence of a blowing agent, producing a final product with a density of 25.6 kg/m3. Alike typical cellular materials the uniaxial compressive behaviour of this material can be described, in terms of stress-strain, by three distinct stages [14]. The first stage — the elastic deformation stage — is followed by a plastic constant stress stage (also known as "plateau" region) where most of the energy absorption occurs. Finally, the material exhibits densification. The elastic part of the behaviour of these materials is mostly due to the axial compressive resistance of the cell walls. The plateau region is mainly related to the bending, crushing and eventually fracture, of the cell walls. The material starts to densify when all the cells are crushed and the

The type of polyurethane foam investigated by Shim *et al.* [45] is adopted for the scope of this study and its stress-strain curve is represented on Figure 1, where the three stages are clearly evident. As the overall behaviour of this material can be divided in three distinct stages, its

stress-strain constitutive modelling can be defined by the following set of equations:

*Eε* if *ε* ∈ [0,*ε*y] (elastic behaviour)

*Eε*<sup>y</sup> if *ε* ∈ [*ε*y,*ε*d] (plastic behaviour, plateau)

, (1)

(*ε*<sup>l</sup> <sup>−</sup> *<sup>ε</sup>*)*<sup>b</sup>* if *<sup>ε</sup>* <sup>∈</sup> [*ε*d,*ε*l] (densification)

where *E* is the material elastic modulus (considered to be *E* = 2.78 MPa), *ε*<sup>y</sup> is the compressive yield strain (*ε*<sup>y</sup> = 0.05), *ε*<sup>d</sup> is the densification strain (*ε*<sup>d</sup> = 0.8), *ε*<sup>l</sup> is the maximum compressive strain (*ε*<sup>l</sup> = 0.95) and *a* and *b* are constants which define the shape of the stress-strain curve in

In previous investigations the authors used a Finite Element Analysis (FEA) approach to study the behaviour of four distinct cellular materials under impact loading in order to evaluate their relative efficiency in terms of crashworthiness applications [40]. The materials tested within these studies were two polymeric foams: polyurethane foam and IMPAXX™ ; a metallic foam: aluminium foam; and a natural cellular material: micro-agglomerated cork. The most relevant mechanical properties of these materials are listed on Table 1, where *ρ*∗ and *E*∗ are the density and elastic modulus of the cellular material, respectively, and *E*, *σ*y and *ν* are the

behaviour approaches the behaviour of a monolithic material [19, 42, 54].

material.

*σ* =

the densification regime.

⎧ ⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

*Eε*y exp

*a*(*ε* − *ε*d)

**3. Crashworthiness efficiency of polyurethane foam**

**Table 1.** Mechanical properties of the polyurethane foam and of other cellular materials used for comparison purposes.

Paulino and Teixeira-Dias[40] proposed a quantitative procedure that allows a padding or protection system designer to determine the crashworthiness efficiency and performance of specific cellular materials. This procedure assumes that the best method to assess the material value for automotive safety applications is by evaluating the rate at which it dissipates energy. In vehicle impacts, the ideal would be for energy to be dissipated in a gradual and controlled manner. Bearing this in mind, the authors proposed and tested a performance index, *φ*, as an attempt to quantitatively evaluate the energy absorption rate of a certain cellular material. The analytical expression that better describes the dependency of the absorbed energy with time during an impact can be given by:

$$E = E(\bar{t}) = \bar{E}\_c^{\min} + \left(\bar{E}\_c^{\max} - \bar{E}\_c^{\min}\right) \left[\frac{\exp\left(\lambda \frac{I - I^{\max}}{I^{\min} - I^{\max}}\right) - 1}{\exp(\lambda) - 1}\right] \tag{2}$$

**Figure 2.** Variation of the performance index *φ* as a function of the initial impact kinetic energy *Eci* for different cellular materials [40]. PUF: polyurethane foam; IMP: IMPAXX™ ; ALF: aluminium foam;

On the Use of Polyurethane Foam Paddings to Improve Passive Safety in Crashworthiness Applications 343

was performed using LS-Dyna™to assess the benefits of including a padding confined in the vehicle's lateral door and compare the efficiency of different paddings made from different cellular materials, i.e. rigid polyurethane foam (PUF), IMPAXX™ (IMP), micro-agglomerated

Three key parameters in terms of crashworthiness are defined and analysed, namely the

The use of a simplified model is a common strategy for cost effective preliminary evaluation of crashworthiness situations [9, 12]. Following this line of thought and in the scope of this investigation, an approximate model to crash tests performed by Euro NCAP [38] is developed, implemented and used for the evaluation of the safety performance in

The generic vehicle tested in this simplified model consists of a subset of elastic spring elements and the lateral door. The subsets of springs are defined in such a way as to approximately describe the behaviour of the remaining structure of the vehicle. For this purpose, the weight of the vehicle and passengers, the vertical position of the centre of gravity of the car and the friction coefficient between the vehiclet's tires and the asphalt are

acceleration profiles, the intrusion levels and the loads acting on the vehicle structure.

MAC: micro-agglomerated cork.

**3.1. Numerical modelling**

vehicle-to-vehicle side-impacts.

cork (MAC) and aluminium foam (ALF).

where *E* = *E*(¯*t*) is the analytical function of the energy absorption in time, *E*min *<sup>c</sup>* is the minimum kinetic energy of an impacting wall and *E*max *<sup>c</sup>* is the maximum kinetic energy of the moving wall. *t* min and *t* max are the minimum and maximum time values considered for the analysis, respectively. The use of the overbar indicates that the respective variable is normalised. *λ* is a dimensionless parameter that defines the shape of the energy absorption curve. The methodology and interpretation of this performance is explained in more detail by Paulino and Teixeira-Dias [40].

On a first analysis, the research carried out by the authors showed that for all the impact loading cases studied polyurethane foam was actually not the best performing cellular material among the ones tested, as can be observed from the results on Figure 2. The four materials investigated share a tendency of decreasing performance index with the increase of initial impact kinetic energy. For all the levels of energy studied PUF has a better behaviour than IMPAXX™. However, for low values of initial impact energy PUF exhibits relatively high values of performance index, being overtaken only by micro-agglomerated cork or aluminium foam. Nonetheless, in the same study it was also verified that the specific energy absorption results of the rigid polyurethane foam tested was higher than aluminium foam and micro-agglomerated cork. In fact, the former was the material with the lowest density (see Table 1). It is then reasonable to assume that for denser foams the results in terms of total absorbed energy, maximum acceleration, average force or performance index could be similar — or even better — to those obtained when using other cellular materials.

The passive safety system proposed to protect the occupant pelvic area from side-impact collision consists of a padding confined inside the vehicle's lateral doors, positioned in the direction of the occupants pelvic area, as can be seen in Figure 3. This protection padding should result in lower forces transmitted to the occupant and lower maximum accelerations due to the material energy absorption capabilities, as explained previously.

Standard side-impact crash tests should be performed in order to make a correct evaluation of the efficiency of polyurethane foam as a material dedicated to energy absorption specifically to improve passive safety in side-impacts. Given the complexity associated to the numerical simulation of crash tests and consequently due to the highly expensive procedures, a simplified model was used to replicate a vehicle-to-vehicle side-impact as defined by the European New Car Assessment Programme (Euro NCAP) [38]. A schematic representation of this simplified model is shown in Figure 4. Within this scope, a set of finite element analyses

342 Polyurethane On the Use of Polyurethane Foam Paddings to Improve Passive Safety in Crashworthiness Applications <sup>7</sup> On the Use of Polyurethane Foam Paddings to Improve Passive Safety in Crashworthiness Applications 343

**Figure 2.** Variation of the performance index *φ* as a function of the initial impact kinetic energy *Eci* for different cellular materials [40]. PUF: polyurethane foam; IMP: IMPAXX™ ; ALF: aluminium foam; MAC: micro-agglomerated cork.

was performed using LS-Dyna™to assess the benefits of including a padding confined in the vehicle's lateral door and compare the efficiency of different paddings made from different cellular materials, i.e. rigid polyurethane foam (PUF), IMPAXX™ (IMP), micro-agglomerated cork (MAC) and aluminium foam (ALF).

Three key parameters in terms of crashworthiness are defined and analysed, namely the acceleration profiles, the intrusion levels and the loads acting on the vehicle structure.

#### **3.1. Numerical modelling**

6 Will-be-set-by-IN-TECH

value for automotive safety applications is by evaluating the rate at which it dissipates energy. In vehicle impacts, the ideal would be for energy to be dissipated in a gradual and controlled manner. Bearing this in mind, the authors proposed and tested a performance index, *φ*, as an attempt to quantitatively evaluate the energy absorption rate of a certain cellular material. The analytical expression that better describes the dependency of the absorbed energy with

where *E* = *E*(¯*t*) is the analytical function of the energy absorption in time, *E*min

for the analysis, respectively. The use of the overbar indicates that the respective variable is normalised. *λ* is a dimensionless parameter that defines the shape of the energy absorption curve. The methodology and interpretation of this performance is explained in more detail by

On a first analysis, the research carried out by the authors showed that for all the impact loading cases studied polyurethane foam was actually not the best performing cellular material among the ones tested, as can be observed from the results on Figure 2. The four materials investigated share a tendency of decreasing performance index with the increase of initial impact kinetic energy. For all the levels of energy studied PUF has a better behaviour than IMPAXX™. However, for low values of initial impact energy PUF exhibits relatively high values of performance index, being overtaken only by micro-agglomerated cork or aluminium foam. Nonetheless, in the same study it was also verified that the specific energy absorption results of the rigid polyurethane foam tested was higher than aluminium foam and micro-agglomerated cork. In fact, the former was the material with the lowest density (see Table 1). It is then reasonable to assume that for denser foams the results in terms of total absorbed energy, maximum acceleration, average force or performance index could be similar

The passive safety system proposed to protect the occupant pelvic area from side-impact collision consists of a padding confined inside the vehicle's lateral doors, positioned in the direction of the occupants pelvic area, as can be seen in Figure 3. This protection padding should result in lower forces transmitted to the occupant and lower maximum accelerations

Standard side-impact crash tests should be performed in order to make a correct evaluation of the efficiency of polyurethane foam as a material dedicated to energy absorption specifically to improve passive safety in side-impacts. Given the complexity associated to the numerical simulation of crash tests and consequently due to the highly expensive procedures, a simplified model was used to replicate a vehicle-to-vehicle side-impact as defined by the European New Car Assessment Programme (Euro NCAP) [38]. A schematic representation of this simplified model is shown in Figure 4. Within this scope, a set of finite element analyses

— or even better — to those obtained when using other cellular materials.

due to the material energy absorption capabilities, as explained previously.

� − 1 ⎤

*<sup>c</sup>* is the maximum kinetic energy of

⎦ (2)

*<sup>c</sup>* is the

exp(*λ*) − 1

max are the minimum and maximum time values considered

time during an impact can be given by:

the moving wall. *t*

Paulino and Teixeira-Dias [40].

*E* = *E*(¯*t*) = *E*¯min

min and *t*

minimum kinetic energy of an impacting wall and *E*max

*<sup>c</sup>* + � *E*¯max *<sup>c</sup>* <sup>−</sup> *<sup>E</sup>*¯min *c* � ⎡ ⎣ exp � *λ* ¯*t*−¯*<sup>t</sup>* max ¯*t*min−¯*t*max

> The use of a simplified model is a common strategy for cost effective preliminary evaluation of crashworthiness situations [9, 12]. Following this line of thought and in the scope of this investigation, an approximate model to crash tests performed by Euro NCAP [38] is developed, implemented and used for the evaluation of the safety performance in vehicle-to-vehicle side-impacts.

> The generic vehicle tested in this simplified model consists of a subset of elastic spring elements and the lateral door. The subsets of springs are defined in such a way as to approximately describe the behaviour of the remaining structure of the vehicle. For this purpose, the weight of the vehicle and passengers, the vertical position of the centre of gravity of the car and the friction coefficient between the vehiclet's tires and the asphalt are

**Figure 4.** Schematic representation of the simplified model used for finite element implementation of a

On the Use of Polyurethane Foam Paddings to Improve Passive Safety in Crashworthiness Applications 345

**Figure 5.** Finite element representation of the simplified model of the vehicle's lateral structure

The designed and proposed padding system was modelled with four-node tetrahedral elements. The material behaviour was described using the \*MAT\_HONEYCOMB constitutive

developed and implemented to simulate the side-impact.

side-impact crash test according to the EuroNCAP standard [38].

**Figure 3.** Illustration of the inclusion and position of the protection padding, confined in the lateral door of the vehicle.

considered. This schematic description is illustrated on Figure 5. This approach is considered satisfactory given that the deceleration and intrusion behaviour of a vehicle during a collision are mostly influenced by the two following structural properties: (i) its mass and (ii) its global stiffness [36]. With this approach it should be possible to assess the efficiency of a given structural component without modelling the full vehicle and still assure reasonable results and precision.

The springs representing the global structure of the vehicle were modelled within LS-Dyna™ using two-node discrete elements and \*MAT\_SPRING\_ELASTIC stiffness response model. Different material stiffness magnitudes were assigned to the springs in accordance to their relative position to the centre of gravity of the vehicle. The vehicle's lateral door was modelled considering four-node fully integrated shell elements implemented with the Belytschko-Tsay formulation [5].

The material considered for the model of the door was DC06 steel, constitutively described with the \*MAT\_PIECEWISE\_LINEAR\_PLASTICITY material model, with an elastic modulus *E* = 210 GPa, density *ρ* = 7850 kg/m<sup>3</sup> and Poisson ratio *ν* = 0.3.

344 Polyurethane On the Use of Polyurethane Foam Paddings to Improve Passive Safety in Crashworthiness Applications <sup>9</sup> On the Use of Polyurethane Foam Paddings to Improve Passive Safety in Crashworthiness Applications 345

8 Will-be-set-by-IN-TECH

**Figure 3.** Illustration of the inclusion and position of the protection padding, confined in the lateral door

considered. This schematic description is illustrated on Figure 5. This approach is considered satisfactory given that the deceleration and intrusion behaviour of a vehicle during a collision are mostly influenced by the two following structural properties: (i) its mass and (ii) its global stiffness [36]. With this approach it should be possible to assess the efficiency of a given structural component without modelling the full vehicle and still assure reasonable results

The springs representing the global structure of the vehicle were modelled within LS-Dyna™ using two-node discrete elements and \*MAT\_SPRING\_ELASTIC stiffness response model. Different material stiffness magnitudes were assigned to the springs in accordance to their relative position to the centre of gravity of the vehicle. The vehicle's lateral door was modelled considering four-node fully integrated shell elements implemented with the Belytschko-Tsay

The material considered for the model of the door was DC06 steel, constitutively described with the \*MAT\_PIECEWISE\_LINEAR\_PLASTICITY material model, with an elastic modulus

*E* = 210 GPa, density *ρ* = 7850 kg/m<sup>3</sup> and Poisson ratio *ν* = 0.3.

of the vehicle.

and precision.

formulation [5].

**Figure 4.** Schematic representation of the simplified model used for finite element implementation of a side-impact crash test according to the EuroNCAP standard [38].

**Figure 5.** Finite element representation of the simplified model of the vehicle's lateral structure developed and implemented to simulate the side-impact.

The designed and proposed padding system was modelled with four-node tetrahedral elements. The material behaviour was described using the \*MAT\_HONEYCOMB constitutive approach in order to describe all three different cellular materials. This material is generally adequate for honeycomb and foam materials with anisotropic behaviour [11, 25, 27]. This modelling approach assumes zero value for the Poisson ratio and considers a variable elastic modulus, increasing linearly from the initial value as a function of the relative volume (i.e. the ratio of the actual volume to the initial volume) up to the fully compacted material modulus.

Furthermore, from *t* ≈ 90 ms on the load almost goes back to zero on all numerical simulations. This is a consequence of the separation of the rigid wall from the impactor. During this stage, however, the system exhibits rigid body motion and, thus, the results obtained for times *t* > 90 ms are not considered relevant for the scope of this research.

On the Use of Polyurethane Foam Paddings to Improve Passive Safety in Crashworthiness Applications 347

It can also be clearly observed that the average load during the considered time interval is considerably lower (≈ 50kN), one order of magnitude, for all the crash tests including a lateral padding when compared the one observed for the test with no padding (≈ 500kN). This leads to the conclusion that the implementation of a padding, either PUF, MAC, IMP or ALF, leads to a much lower and smoother distribution of the load for the whole duration of the impact. The average force obtained for the simulations with the protection padding was around 85% lower than the ones obtained without padding and the maximum force was up to 79% lower.

**Figure 6.** Evolution of the reaction force on the moving rigid wall with time for the simulations of

The evolution of the kinetic energy of the whole system with time is represented on Figure 7. A sudden increase of the kinetic energy can be observed for *t* ≈ 3 ms for the crash test with no padding. This corresponds to the instant at which the impactor structure initiates contact with the door of the vehicle. Additionally, for all the simulations performed the curves exhibit an inflection near the final stage of the impact (*t* ≈ 80 ms), increasing from this instant until the

side-impact crash tests.

**4.2. Kinetic energy**

According to the EuroNCAP standards [38] the impacting vehicle (see Figure 4) must be modelled considering deformable 3030 and 5052 aluminium honeycomb blocks. These blocks should be attached to a mobile structure that is to be considered rigid. Within the scope of this work the deformable blocks were modelled using eight-node hexahedral finite elements. The material behaviour was once again described by the \*MAT\_HONEYCOMB constitutive model, for the same reasons stated for the padding materials. The necessary material properties were determined considering both honeycombs [14]. The propeller structure is, however, fairly complex according to EuroNCAP regulations and it is not fully described on the side-impact protocols available. Nonetheless, the total weight of the impactor system is known and, ultimately, the geometry of the impactor moving structure is not significantly relevant for the conditions of the performed tests. For this reason this moving structure was modelled as a moving rigid wall. The most determinant feature is the part of the impactor colliding with the vehicle's lateral door, i.e., the deformable aluminium honeycomb blocks. Hence, mass was added to the impactor's anterior part and the initial velocity of the crash tests (*v*<sup>0</sup> = 13.89 m/s) was assigned to the structure.
