A stochastic computational method for evaluation of global and local behavior of random elastic media

A stochastic computational method is developed to evaluate global effective properties and local probabilistic behavior of random elastic media. The elasticity solution for random media is addressed with a method that combines a fast iterative numerical method with stochastic decomposition techniques. Stochastic homogenization problems are mathematically formulated with an ensemble average approximation scheme based on a concept of stochastic representative volume element (SRVE). Probabilistic descriptors of local strain are generated based on convolution equations derived from the equilibrium equations of elasticity. With the application of the Galerkin formulation in probability space and the Fourier transform of the convolution equations, an efficient numerical scheme is implemented using an iterative algorithm that takes advantage of fast Fourier transform. Two algorithms are provided for Gaussian and non-Gaussian random media, respectively, with corresponding sufficient conditions for convergence derived. Finally, numerical experiments are conducted for a Gaussian and a non-Gaussian random medium, respectively, with verifications obtained from Monte Carlo simulation.