A Three-Dimensional Unit Cell Model With Application Toward Particulate Composites

Abstract

A formulation of a fully three-dimensional unit cell model is presented for uniform general deformation at a point in a composite material. The unit cell model is constructed as a finite element discretization of the unit cube. General displacement periodicity boundary conditions are prescribed such that the cell may be considered as a representative volume element of material. As a particular application of the model, the problem of determining the least anisotropic periodic model of a particulate composite is considered, and comparisons are made with bounds for elastic two-phase composites possessing cubic symmetry.