2 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 a nd composite) materials by combining asymptotic homogenization theory with the Voronoi Cell finite element model (VCFEM). VCFEM for microstr uctural modeling originates from Dirichlet tessellation of representat ive material elements at sampling points in the structure. Structural modeling is done by the general purpose finite element code ABAQUS, an d interfacing with the microscale VCFEM analysis is done through the u ser subroutine in ABAQUS for material constitutive relation, UMAT. Asy mptotic homogenization in UMAT generates macroscopic material paramete rs for ABAQUS. Following the macroscopic analysis, a local VCFEM analy sis is invoked to depict the true evolution of microstructural state v ariables. Various numerical examples are executed for validating the e ffectiveness of VCFEM-HOMO, and the effect of size, shape and distribu tion of heterogeneities on local and global response is examined.