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

TL;DR

This paper introduces stochastic models for crack development in 1D and 2D brittle solids, predicting power-law fragment size distributions and analyzing different crack interaction scenarios.

Contribution

It provides new stochastic models for brittle fragmentation in one and two dimensions, including analytical results and power-law distribution predictions.

Findings

Power-law size distributions for certain fragmentation scenarios

Analytical results for crack development observables

Distinct models for interacting and non-interacting fragments

Abstract

Stochastic models for the development of cracks in 1 and 2 dimensional objects are presented. In one dimension, we focus on particular scenarios for interacting and non-interacting fragments during the breakup process. For two dimensional objects, we consider only non-interacting fragments, 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.