Numerical Approximation of Stochastic Systems for Composite Materials Based on Markov Chains

摘要

The crack density and crack growth rate are important parameters which are used to describe the fatigue damage and predict fatigue life of a composite material. Even the same good manufacturing practice, the fatigue damage of materials may be different. Also material properties often accompany random fluctuation. Thus stochastic systems are used to present the crack density and crack growth rate. It is surprising that there are not any numerical schemes established for hybrid stochastic systems in composite materials. In this paper, based on Markov chains, the Euler-aruyama method is developed, and the main aim is to show the convergence of the numerical solutions under the non-Lipschitz condition for hybrid stochastic material systems.