Computational Elucidation of Elastic Percolation Threshold in Isotropic and Anisotropic Microstructures with Voronoi Tessellation

Abstract

In this paper, the mechanical properties of randomly shaped microstructures containing two different elastic materials are investigated. Representative volume elements (RVE) containing random tessellations were created using a random generating procedure. The procedure divides the RVE surface by Voronoi tessellations and the elastic behavior of the surface is analyzed under tensile and shear deformations using the finite element method (FEM). Components of stress tensor for each element obtained from FE analysis were used to compute the overall elastic properties of the microstructure. Percolation threshold was defined based on the instantaneous gradient of the tensile and shear modulus diagrams. Numerical results reveal that the percolation thresholds in tensile and shear modes for isotropic RVE are almost the same while there is a remarkable difference between percolation thresholds for an anisotropic case. Furthermore, in the procedure performed in this study, a distinct inconsistency in elastic properties of anisotropic microstructure in longitudinal and transverse directions is observed. The mentioned method presents a paradigmatic overview for generating random isotropic and anisotropic tessellations with different aspect ratios on microstructures and evaluating their overall properties and percolation limit for them.