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.

Expanded polystyrene foams are widely used materials for various applications in engineering, including their use for protective designs. For this type of application, in engineering analysis and design, it is required to know the mechanical response to compression of this type of material, since energy parameters that support the analysis of the effectiveness of a design are derived from it. One of these parameters is strain hysteresis, through which it is possible to know how capable a material is of absorbing energy. The modeling and prediction of this parameter is a challenge from the analysis point of view. This contribution presents a method based on feed-forward artificial neural network models that address a modeling approach to derive this parameter from the mechanical response of expanded polystyrene foam. From this, models are constructed that can predict the response of such material to various density and loading rate conditions. The best of a total of 30 neural network models, which are capable of deriving energy parameters such as hysteresis, is chosen. The results show that this approach is valid for the deformation energy analysis of expanded polystyrene foams since results consistent with the material phenomenology and errors of less than 3% with respect to experimental data are obtained.

Traditional modeling of mechanical energy absorption due to compressive loadings in expanded polystyrene foams involves mathematical descriptions that are derived from stress/strain continuum mechanics models. Nevertheless, most of those models are either constrained using the strain as the only variable to work at large deformation regimes and usually neglect important parameters for energy absorption properties such as the material density or the rate of the applying load. This work presents a neural-network-based approach that produces models that are capable to map the compressive stress response and energy absorption parameters of an expanded polystyrene foam by considering its deformation, compressive loading rates, and different densities. The models are trained with ground-truth data obtained in compressive tests. Two methods to select neural network architectures are also presented, one of which is based on a Design of Experiments strategy. The results show that it is possible to obtain a single artificial neural networks model that can abstract stress and energy absorption solution spaces for the conditions studied in the material. Additionally, such a model is compared with a phenomenological model, and the results show than the neural network model outperforms it in terms of prediction capabilities, since errors around 2% of experimental data were obtained. In this sense, it is demonstrated that by following the presented approach is possible to obtain a model capable to reproduce compressive polystyrene foam stress/strain data, and consequently, to simulate its energy absorption parameters.