Discrete modeling of elastic heterogeneous media

Discrete models provide advantages in simulating fracture in quasi-brittle materials due, in part, to their simplicity in representing cracking and other forms of displacement discontinuity. However, the stress analyses that form the basis for fracture simulation are complicated by difficulties in modeling the Poisson effect and other aspects of elastic behavior. The capabilities of Voronoi-cell lattice models, which are a form of particle-based lattice model, for elastic stress analysis are evaluated. It is found that the conventional means for representing the Poisson effect in particle-based lattice models result in spatially correlated stress oscillations that, at first glance, mimic the effects of material heterogeneity. The correlation length is dependent on discretization size. Alternatively, material heterogeneity can be introduced into elastically uniform lattice models via random assignments of material properties, independent of mesh size and geometry.