The expanded polystyrene foam is widely used as a protective material in engineering applications where energy absorption is critical for the reduction of harmful dynamic loads. However, to design reliable protective components, it is necessary to predict its nonlinear stress response with a good approximation, which makes it possible to know from the engineering design analysis the amount of energy that a product may absorb. In this work, the hyperfoam constitutive material model was used in a finite element model to approximate the mechanical response of an expanded polystyrene foam of three different densities. Additionally, an experimental procedure was performed to obtain the response of the material at three loading rates. The experimental results show that higher densities at high loading rates allow better energy absorption in the expanded polystyrene. As for the energy dissipation, high dissipation is obtained at higher densities at low loading rates. In the numerical results, the proposed finite element model presented a good performance since root mean square error values below 9% were obtained around the experimental compressive stress/strain curves for all tested material densities. Also, the prediction of energy absorption with the proposed model was around a maximum error of 5% regarding the experimental results. Therefore, the prediction of energy absorption and the compressive stress response of expanded polystyrene foams can be studied using the proposed finite element model in combination with the hyperfoam material model.

In this study, a comparison between the well-established Lagrangian approach and the Arbitrary Lagrangian–Eulerian (ALE) approach is presented. This comparison aims to verify the ALE's approach suitability for modeling thermomechanical processes. After that, a study on the material's stress state evolution inside the specimen is provided. The stress state is evaluated through the triaxiality factor and Lode parameter. Ideally, under pure compression, these parameters' values are − 1/3 and − 1, respectively. However, it is not possible to achieve ideal conditions in actual experiments. The Lagrangian model was done in QForm, and the ALE model was done in LS-Dyna. The results from both models are in good agreement between them and agree with the force vs. stroke measured during the experiments. Two paths were defined to study the stress state inside the sample, in the radial direction (equator line) and axial direction (axial line). It was concluded that some areas in both paths might be considered as approximately under pure compression stress state. In addition, the ALE approach accuracy for thermomechanical modeling was verified.