A MODEL FOR ANALYSIS OF ARBITRARY COMPOSITE AND POROUS MICROSTRUCTURES WITH VORONOI CELL FINITE ELEMENTS

The Voronoi Cell Finite Element Model (VCFEM) has been successfully developed for materials with arbitrary microstructural distribution. In this method, the finite element mesh evolves naturally by Dirichlet Tessellation of the microstructure. Composite VCFEM for small deformation plasticity has been developed by expressing the element stresses in terms of polynomial expansions of location co-ordinates. Though this works well for discrete composites with inclusions, its effectiveness diminishes sharply for porous materials with voids. The effect worsens sharply with voids of arbitrary shapes. To overcome this limitation, a new way of defining stress functions is introduced in this paper. Based on a transformation method similar to the Schwarz-Christoffel conformal mapping, it introduces reciprocal stress functions that are derived to incorporate shape effects. Several numerical experiments are conducted to establish the strength of this formulation. The effect of various microstructural morphologies on the overall response and local variables are studied