Cellular automaton for the fracture of disordered media

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 $\scriptstyle 2.$