A stress-driven computational homogenization method based on complementary potential energy variational principle for elastic composites

Abstract

Based on the complementary potential energy variational principle, in this work, we proposed a stress-driven homogenization procedure to compute overall effective material properties for elastic composites with locally heterogenous micro-structures. We have developed a novel incremental variational formulation for homogenization problems of both infinitesimal and finite deformations where the macro-stress-based complementary potential energy is obtained for hyperelastic materials for a global minimization problem with respect to fine-scale displacement fluctuation field. The point of departure of our approach is a general complementary variational principle formulation that can determine material responses of elastic composites with heterogeneous micro structures. We have implemented the proposed stress-driven computational homogenization procedure with the finite element method. By comparing the numerical results with the analytical method and the strain-driven homogenization method, we find that the stress-driven homogenization offers the lower bound estimate of materials properties for elastic composites.