On macroscopic elastic properties of isotropic discrete systems: effect of tessellation geometry

Abstract

Discrete mesoscale models of heterogeneous materials attracts increased attention thanks to their robustness, relative simplicity and direct representation of complex phenomena taking place during fracture initiation and propagation. Their major drawback is limitations imposed on macroscopic Poisson's ratio, thus they can be used only for material with low Poisson's ratio.The contribution develops analytical formulas for estimation of macroscopic Poisson's ratio of two dimensional isotropic discrete systems where artificial distribution of angle between contact vectors and contact facets is assumed. The analytical formulas unfortunately lead to conclusion that the Poisson's ratio cannot be increased by model geometrical changes. The widest range of possible Poisson's ratio is obtained for perpendicular contact vector and contact facet, i.e. for the models used in most of the literature on this topic.