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.

聚合物泡沫广泛用于许多冲击保护应用，具有密度梯度策略的功能梯度泡沫材料因其灵活和可设计的能量吸收应用而受到越来越多的研究。本研究旨在开发一种分析模型来预测功能梯度聚合物泡沫 (FGPF) 在单轴压缩载荷下的响应。发泡聚苯乙烯 (EPS) 是最常见的聚合物泡沫，在本研究中被选为代表性泡沫。首先开发了单轴压缩下均匀密度EPS泡沫的本构模型，然后通过单轴准静态和动态压缩实验进行了验证。基于 FGPF 是许多独立的均匀密度 EPS 泡沫层的组合的假设，采用理想的刚性-完美塑性锁定 (R-PP-L) 模型来开发分析模型，用于预测单轴压缩载荷下 FGPF 的应力-应变相关性。基于经过验证的EPS泡沫本构模型，还建立了FGPF有限元模型对解析模型进行验证。结果表明，该分析模型可用于预测 FGPF 在低到中等应变率 (10^-3 s ^-1 ∼ 10 ² s ^-1 )。该研究还表明，可以使用优化方法设计 FGPF，以最大限度地提高其耐撞性能。所提出的分析方法和优化程序可用于其他功能梯度泡沫材料。