Numerical simulation of nonlinear behavior in porous materials using 3D VCFEM formulated with plasticity and temperature-dependent thermal expansion

Porous materials in industrial applications are often exposed to complex environments, leading to nonlinear behaviors such as plastic strain and temperature-dependent thermal expansion. The nonlinear behaviors can significantly impact other aspects such as the strength and structural stability of porous materials. Traditional finite element methods, when applied to simulate the nonlinear behavior of porous materials in industrial applications, typically require a large number of elements and multiple increments to achieve the desired accuracy, resulting in high computational costs and low efficiency. This paper presents a three-dimensional Voronoi cell finite element method (3D VCFEM) that integrates the three-dimensional stress hybrid element method, variational principles, and incremental theory of plasticity. This method is specifically designed to simulate the nonlinear behaviors in porous materials that exhibit plasticity and temperature-dependent thermal expansion in complex environments. Based on the principle of minimum complementary energy and the incremental theory of plasticity, a modified complementary energy functional considering temperature-dependent thermal expansion is derived. Then propose the solvation of displacement interpolation function, constructing a three-dimensional stress function that accounts for ellipsoidal pores. The stress calculation results of 3D VCFEM are compared with those of MSC MARC. This study demonstrates that the 3D VCFEM offers significant advantages in predicting the stress distribution of porous materials in complex environments, achieving high accuracy while significantly reducing computational costs.