Numerical modelling of rock materials with polygonal finite elements

Abstract

This article presents some preliminary results on numerical modeling of rock ma-
terials with polygonal finite elements. A method to describe the rock microstructure based on
Voronoi diagrams, representing the rock grain texture, is sketched. In this method, the minerals
constituting the rock are represented as Voronoi cells which themselves are polygonal finite ele-
ments. A three-point bending problem under plane stress linear elasticity condition is solved in
order to compare the performance of polygonal elements to ordinary finite elements. Moreover,
it is demonstrated by solving the stress state in uni-axial compression that the heterogeneity
described with the present method results in short-range tensile stresses which could initiate
mode-I cracks.