Voronoi-based discretizations for fracture analysis of particulate materials

Damage and mass transport behavior of particulate materials depend on the spatial distribution and orientation of the phase fractions and the properties of their interfaces. Discretization of this three-dimensional setting is the first critical step in the modeling of such behavior. In this paper, a general procedure is developed for discretizing particulate materials, such as particles embedded within a cementing matrix, in which the particle inclusions are assumed to be randomly generated polyhedra. Polyhedron discretization is based on the Voronoi tessellation of a set of points, which is obtained through a multistep process that relies on the concept of point saturation. The matrix–particle and/or particle–particle interfaces are explicitly constructed. To demonstrate the utility of the approach, uniaxial tensile tests (of a single particle, embedded in a matrix) are simulated using a lattice model. It is seen that interface debonding is strongly affected by inclusion shape and orientation with respect to the tension field. A procedure is developed for the discretization and analysis of multi-particle systems.