Stochastic Morphological Modeling of Random Multiphase Materials

Abstract

A short-range-correlation (SRC) model is introduced in the framework of Markov/Gibbs random field theory to characterize and simulate random media. The Metropolis spin-flip algorithm is applied to build a robust simulator for multiphase random materials. Through development of the SRC model, several crucial conceptual ambiguities are clarified, and higher-order statistical simulation of random materials becomes computationally feasible. In the numerical examples, second- and third-order statistical simulations are demonstrated for biphase random materials, which shed light on the relationship between nth-order correlation functions and morphological features. Based on the observations, further conjectures are made concerning some fundamental morphological questions, particularly for future investigation of physical behavior of random media. It is expected that the SRC model can also be extended to third- and higher-order simulations of non-Gaussian stochastic processes such as wind pressure, ocean waves, and earthquake accelerations, which is an important research direction for high fidelity simulation of physical processes.