Cellular Automata Computer Model of Polycrystalline Plastic Deformation

"A cellular model of the plastic deformation of polycrystalline aggregate is proposed and comprehensively described. Representative volume element (RVE) of a solid body, that is being deformed, is described as a population of interconnected units that, in turn, can consist of lower scale level units. Sliding along the various allowed sliding systems deforms simple units, which do not have an internal structure. For consideration of stress distribution within the limits of components, the approach of self-consistent field is used. Rotation of units and moment stresses connected with it are taken into account. Results of computer experiments are analyzed.1. IntroductionMicromechanical models of polycrystals are a link between the research of plastic deformation on micro and macro levels. Computer simulation of inelastic strain of polycrystals has found a great deal of interest as well. Despite the fact that this approach does not allow to obtain macroscopic constitutive relationships that are used in deformed solid body mechanics, it clarifies essential features of the phenomena in many aspects. First of all, it concerns effects stipulated by interdependence of micro-level and macro level of plastic deformation processes. Also, with the computing mechanics, instead of constitutive relationships, the adequate computer models can be used. Broad possibilities for computer simulation of various processes are opened by cellular automata approach. By means of numerical experiments, the cellular automata allows to study the macro behavior of the whole ensemble of cells depending on the local microscopic laws that define evolution of each cell and its interaction with the closest environment.We propose a mathematical model of a polycrystalline aggregate (the cellular model) based on a self-consistent scheme and on the interaction law similar to the one by Berveiller and Zaoui [1]. Our original solution is the self-similar structure of cellular automata that allows modeling of the fractal nature of real materials (Figure 1). The goals of this work are to present the major structures and relations of cellular model of polycrystal and to test this model for its adequacy as for describing known effects and dependencies. Identification of the model and its application for studying of concrete polycrystals are put aside for the future research."