Simple Stochastic Models for Material Failure

Abstract

A variety of simple models for material failure and deformation have been developed in recent years. These models are closely related to and were in part motivated by diffusion-limited aggregation model and other models for non-equilibrium pattern formation. Here several related models for crack growth are described. In a model closely related to DLA the effective fractal dimensionality appears to depend on local boundary conditions as well as on the dependence of the growth probabilities on the local stress and strain. The dependence on local boundary conditions is surprising and may be a consequence of finite size effects. If the growth probabilities are represented by an inhomogeneous power law then crossover effects that depend on the boundary conditions are found. Such effects are also expected for other models such as DLA and dielectric breakdown models. Some recent work concerning models for surface cracking and models with non-central forces are also surveyed. These simple models raise important theoretical questions that may lead to a better understanding of real materials. Improved algorithms for the efficient relaxation of elastic networks are needed for models of this type to continue to complement experimental and theoretical work in a strongly synergistic fashion.KeywordsTriangular LatticeBond BreakingBreak BondMaterial FailureSurface BondThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.