DISCRETE MODELS FOR 2-DIMENSIONAL AND 3-DIMENSIONAL FRAGMENTATION

We study an iterative stochastic process as a model for two- and three -dimensional discrete fragmentation. The model fulfills mass conservat ion and is defined on two- and three-dimensional lattices of linear si ze 2(n). At each step of the process the ''most stressed'' piece is br oken in the direction of the maximum net force, which is a random vari able. Despite their simplicity, reflected in deterministic fracture cr iteria and simple random forces acting on the materials, our models pr esent complex features that reproduce some of the experimental results that have been obtained. For some regimes a log-normal and a power la w behavior are obtained for the fragment size histogram. For this reas on we propose them as basic models that can be substantially refined t o describe the fragmentation process of more realistic models.