Response of functionally graded polymeric foam under axial compression

Polymeric foams are widely used for many impact protection applications, and functionally graded foam materials with density-gradient strategies have been increasingly studied for their flexible and designable energy absorption applications. This study aims to develop an analytical model to predict the responses of functionally graded polymeric foam (FGPF) under uniaxial compression loads. The expanded polystyrene (EPS), which is the most common polymeric foam, was selected as a representative foam in this study. The constitutive model for uniform-density EPS foam under uniaxial compression was first developed and then validated by the uniaxial quasi-static and dynamic compression experiments. Based on the assumption that FGPF is a combination of numerous independent uniform-density EPS foam layers, the idealised rigid-perfectly plastic-locking (R-PP-L) model was adopted to develop an analytical model for predicting the stress-strain correlations of FGPF under uniaxial compressive loads. Based on the validated constitutive model of EPS foam, the FGPF finite element model was also established to validate the analytical model. It is demonstrated that the analytical model can be applied to predict the compressive stress-strain relations of FGPF under the loading conditions of low to moderate strain-rates (10⁻³ s⁻¹ ∼ 10² s⁻¹). This study also showed that FGPF can be designed using the optimization method to maximise its crashworthiness performance. The proposed analytical method and the optimization procedure could be used for other functionally graded foam materials.