A three-dimensional VCFEM formulated with elasticity and thermal strain for porous materials

In predicting the stress distributions of porous materials, the unique pore microstructure significantly impacts the stress distribution results. Traditional finite element methods (FEMs) typically require a large number of meshes to achieve a certain level of accuracy, leading to more degrees of freedom to be computed thus reducing efficiency. This paper proposes a three-dimensional Voronoi cell FEM (3D VCFEM) for porous materials that considers both elasticity and thermal strain using the three-dimensional hybrid stress element method and variational principles. Based on the principle of minimum complementary energy, modified complementary energy functionals are derived for cases with and without thermal strain. After scaling the elements, using the Delaunay division method to subdivide the pore element into multiple Delaunay tetrahedra, integration is performed using the Hammer numerical integration method. A three-dimensional stress function considering ellipsoidal shapes is constructed. By assuming and solving a higher-order stress field within the element, the stress calculation results of VCFEM are compared with those from MSC MARC to verify the accuracy and efficiency of VCFEM, and the innovative features and significant contributions of the three-dimensional VCFEM are also elaborated upon.