3D micromechanical finite element homogenization for predicting effective thermomechanical properties of architected metamaterials and polyurethane foams

This paper presents a three-dimensional micromechanical finite element (FE) homogenization framework for predicting the effective thermomechanical properties of polyurethane (PU) foams and 3D-printed polylactic acid (PLA) architected cellular materials. Representative volume elements (RVEs) subjected to periodic boundary conditions (PBCs) and satisfying the Hill–Mandel macro-homogeneity condition are used to evaluate the elastic and thermal response of different cellular topologies, including honeycomb, re-entrant (auxetic), star-shaped, and stochastic foam structures. The entire modeling workflow is driven by Python scripts integrated with the Abaqus finite element solver, enabling automated generation of RVEs, implementation of (PBCs), and efficient extraction of homogenized properties. The numerical framework is validated against available experimental and numerical results, showing good agreement in the predicted mechanical and thermal properties. The results further demonstrate that increasing relative density enhances load-bearing capacity and thermal transport while reducing stress, strain, and thermal localization. In addition, the studied architectures exhibit anisotropic behavior and direction-dependent heat transfer, with honeycomb and auxetic configurations providing a wide range of effective properties. The proposed framework provides an efficient computational tool for the analysis and design of multifunctional cellular materials.