Discrete models for two- and three-dimensional fragmentation

We study an iterative stochastic process as a model for two- and three-dimensional discrete fragmentation. The model fulfills mass conservation and is defined on two- and three-dimensional lattices of linear size 2n. At each step of the process the “most stressed” piece is broken in the direction of the maximum net force, which is a random variable. Despite their simplicity, reflected in deterministic fracture criteria and simple random forces acting on the materials, our models present complex features that reproduce some of the experimental results that have been obtained. For some regimes a log-normal and a power law behavior are obtained for the fragment size histogram. For this reason we propose them as basic models that can be substantially refined to describe the fragmentation process of more realistic models.