Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model

In this paper, a multiple scale finite element model (VCFEM-HOMO) has been developed for elastic-plastic analysis of heterogeneous (porous and composite) materials by combining asymptotic homogenization theory with the Voronoi Cell finite element model (VCFEM). VCFEM for microstructural modeling originates from Dirichlet tessellation of representative material elements at sampling points in the structure. Structural modeling is done by the general purpose finite element code ABAQUS, and interfacing with the microscale VCFEM analysis is done through the user subroutine in ABAQUS for material constitutive relation, UMAT. Asymptotic homogenization in UMAT generates macroscopic material parameters for ABAQUS. Following the macroscopic analysis, a local VCFEM analysis is invoked to depict the true evolution of microstructural state variables. Various numerical examples are executed for validating the effectiveness of VCFEM-HOMO, and the effect of size, shape and distribution of heterogeneities on local and global response is examined.