A Review of Computational Stochastic Elastoplasticity

Abstract

Heterogeneous materials at the micro-structural level are usually subjected to several uncertainties. These materials behave according to an elastoplastic model, but with uncertain parameters. The present review discusses recent developments in numerical approaches to these kinds of uncertainties, which are modelled as random elds like Young's modulus, yield stress etc. To give full description of random phenomena of elastoplastic materials one needs adequate mathematical framework. The probability theory and theory of random elds fully cover that need. Therefore, they are together with the theory of stochastic nite element approach a subject of this review. The whole group of di erent numerical stochastic methods for the elastoplastic problem has roots in the classical theory of these materials. Therefore, we give here the classical formulation of plasticity in very concise form as well as some of often used methods for solving this kind of problems. The main issues of stochastic elastoplasticity as well as stochastic problems in general are stochastic partial di erential equations. In order to solve them we must discretise them. Methods of solving and discretisation are called stochastic methods. These methods like Monte Carlo, Perturbation method, Neumann series method, stochastic Galerkin method as well as some other very known methods are reviewed and discussed here