Three dimensional Voronoi cell finite element model for microstructures with ellipsoidal heterogeneties

In this paper a three-dimensional Voronoi cell finite element model is developed for analyzing heterogeneous materials containing a dispersion of ellipsoidal inclusions or voids in the matrix. The paper starts with a description of 3D tessellation of a domain with ellipsoidal heterogeneities, to yield a 3D mesh of Voronoi cells containing the heterogeneities. A surface based tessellation algorithm is developed to account for the shape and size of the ellipsoids in point based tessellation methods. The 3D Voronoi cell finite element model, using the assumed stress hybrid formulation, is developed for determining stresses and displacements in a linear elastic material domain. Special stress functions that introduce classical Lame functions in ellipsoidal coordinates are implemented to enhance solution convergence. Numerical methods for implementation of algorithms and yielding stable solutions are discussed. Numerical examples are conducted with inclusions and voids to demonstrate the effectiveness of the model.