Voronoi Cell Finite Element Model for Thermoelastoplastic Deformation in Random Heterogeneous Media

A finite element model has been developed for analysis of heterogeneous media, in which second phase inclusions are arbitrarily dispersed within a matrix. A mesh generator based on Dirichlet tessellation, discretizes the heterogeneous domain, accounting for the arbitrariness in location, shape and size of the second phase. This results in a network of convex “Voronoi” polygons which form the elements in a finite element mesh. An assumed stress hybrid formulation has been implemented for accommodating arbitrary multi-sided elements in the finite element model. Composite element formulations have been developed to incorporate the effect of second phase within each element. Formulations have been developed for thermo-elasticity, micropolar elasticity and elasto-plasticity.