Cellular automaton for the fracture of disordered media

TL;DR

This paper presents a numerical study of crack growth in disordered media using cellular automata, demonstrating fractal crack patterns and an efficient parallel algorithm for large-scale simulations.

Contribution

It introduces a fast, data-parallel algorithm for simulating crack growth in elastic media, enabling large-scale fractal pattern analysis.

Findings

Cracks exhibit fractal patterns with dimension between 1 and 2.

The fractal dimension depends on the breaking criterion used.

Large-scale simulations are feasible on parallel computers like the Connection Machine.

Abstract

We study numerically the growth of a crack in an elastic medium under the influence of a travelling shockwave. We describe the implementation of a fast algorithm which is perfectly suited for a data parallel computer. Using large scale simulations on the Connection Machine we generate cracks with more than 10000 sites on a $\scriptstyle 1024 \times 1024$ lattice. We show that the resulting patterns are fractal with a fractal dimension that depends on the chosen breaking criterion and varies between $\scriptstyle 1.$ and $\scriptstyle 2.$