Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi Cell finite element method Original Research Article

In this paper, a Voronoi Cell finite element method is developed to solve small deformation elastic-plasticity problems for arbitrary heterogenous materials. Dirichlet Tessellation of microstructural representative materials results in a network of arbitrary-sided polygons called Voronoi cells. Each Voronoi cell encompasses one second phase heterogeneity at most. These are natural elements for the microstructure, representing 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. Furthermore, 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 representative material elements.