Prediction of effective properties for random heterogeneous materials with extrapolation

Abstract

This work presents an efficient method to predict effective thermo-mechanical properties of random heterogeneous materials, with the purpose of reducing the cost of computation. The method is applied to morphologically realistic microstructures generated by a modified random morphology description functions algorithm. To achieve this purpose, firstly the convergence rates of the approximate effective material properties by homogenization with increasing cell domain size are numerically investigated, and it shows first-order accuracy of the approximate effective material properties. Secondly, Richardson extrapolation technique is introduced to obtain more accurate approximations of effective material properties by using some smaller cell domains, without the need for computations in larger cell domain. Numerical examples demonstrate that the method significantly saves computation time and computer memory while improving the accuracy of the effective material properties.