A microstructure based numerical method for constitutive modeling of composite and porous materials

An elastic–plastic constitutive model that incorporates the details of material microstructure, is proposed for modeling composite and porous materials. It is based on two-scale analysis using the asymptotic homogenization method and the Voronoi cell finite element model for detailed microstructural analysis. The linear elastic behavior is represented by an orthotropic elasticity tensor, obtained by solving an elastic microstructural problem with periodicity boundary conditions followed by homogenization. In the isotropic hardening plasticity with associate flow rule representation, a pressure-dependent yield function with strain and plastic work dependent parameters is postulated. The variation of these parameters are determined from a numerical database in the strain space that is generated from an ordered sequence of microstructural RVE (representative volume element) analyses with asymptotic homogenization. Numerical examples are conducted to examine the effectiveness of the constitutive model by comparing results of macroscopic analysis using the model and those of incremental two-scale analysis with homogenization. For a wide range of microstructures and loading conditions, the proposed model is found to yield extremely accurate solutions. Considerable advantage is achieved with respect to computational efficiency.