Simulation of ideal material blocks using cellular automata

Abstract

We consider deterministic and probabilistic cellular automata to study and describe certain types of patterns in idealized material blocks. We have partic- ular interest in patterns similar to fractures. The inter- nal structure of these material blocks is assumed to be unknown and probabilistic cellular automata are used to obtain distributions for the referred internal struc- ture. We consider the 1D case. Certain deterministic elementary rules are identified as elementary ideal frac- ture rules and the probabilistic rules are introduced as probabilistic interpolation of these elementary rules. The initial conditions are obtained from the visible bor- ders of the surface (2D block). Therefore, each visible edge is giving additional information and a probabilis- tic fracture type pattern. Different methods to combine these patterns, into a final one, are discussed. Moreover, we introduce refinement techniques of the CA rules to improve the probabilities distributions. This refine- ment process may consider prescribed behaviour or empirical data, and, therefore, the CA rules behaviour becomes adjustable.