New Approach to Bounding Effective Properties of Random Heterogeneous Materials

Abstract

A new approach to bounding effective properties of random heterogeneous materials is developed in this paper. The expectation material properties are computed for a stochastic unit cell to represent the random heterogeneous materials. This stochastic unit cell is then used to compute the upper bound and lower bound of effective properties using the variational asymptotic method for unit cell homogenization, a recently developed general-purpose micromechanics code. In comparison with other approaches, the present approach has two main advantages. 1) The numerical implementation is not restricted to statically homogeneous and isotropic microstructures. 2) Both the lower bound and upper bound converge to the effective properties of a deterministic unit cell with decreasing randomness of the stochastic unit cell. To illustrate the application of this new approach, various examples are analyzed and compared with existing theories.