Schematic models for fragmentation of brittle solids in one and two dimensions

Stochastic models for the development of cracks in 1D and 2D objects are presented. In one dimension, we focus on particular scenarios for interacting fragments (IF1) and non-interacting fragments (NIF1) during the breakup process. For 2D objects, we consider only NIF1, but analyze isotropic and anisotropic development of fissures. Analytical results are given for many observables. Power-law size distributions are predicted for some of the fragmentation pictures considered.