ELASTIC-PLASTIC ANALYSIS OF ARBITRARY HETEROGENEOUS MATERIALS WITH THE VORONOI-CELL FINITE-ELEMENT METHOD

In this paper, a Voronoi Cell finite element method is developed to so lve small deformation elastic-plasticity problems for arbitrary hetero genous materials. Dirichlet Tessellation of microstructural representa tive materials results in a network of arbitrary-sided polygons called Voronoi cells. Each Voronoi cell encompasses one second phase heterog eneity at most. These are natural elements for the microstructure, rep resenting the basic structural elements of the material. In this paper , formulations are developed for directly considering Voronoi cells as elements in a finite element model without any further dissection. Fu rthermore, a composite Voronoi Cell finite element method is developed to account for the presence of the second phase within each polygonal element. Various numerical elastic-plastic examples are executed for validating the effectiveness of this formulation. Finally, studies are conducted to understand the effect of size, shape and distribution of second phase on the averaged and true local responses of representati ve material elements.