A cellular automaton-based technique for modeling mesoscale damage evolution

Abstract

A 2D stochastic cellular automaton model was developed to create a framework to examine the evolution of damage on the mesoscale. The model is based on an expanding representative volume element (RVE) in a cellular domain. The state of a cell, which can be either solid material or void, is determined by mapping existing voids through plastic convection and creating new damage through the cellular automaton. The cellular automaton formulation addresses the effect of damage initiation, propagation and coalescence through the iterative evaluation of individual cells based on their current state and the current states of their eight neighboring cells. The amount of damage in each time step is controlled by conservation of mass in the expanding RVE. By modifying the ratio of damage to plastic convection and the probabilities in the cellular automaton rule table, the model can generate microcrack or microvoid damage morphologies at different spatial scales. Very rapid simulations are achieved using this formulation. Thus, a wide range of material damage morphologies can be rapidly modeled in a single simulation architecture based solely on local cell geometry. However, one will be able to characterize cellular automaton rules and parameters to simulate specific constitutive models of material damage and fracture.