A New Approach to Bounding Effective Properties of Random Heterogeneous Materials

Abstract

A new approach to bounding efiective properties of random heterogeneous materials is developed using the variational asymptotic method. First, the expectation material properties are computed for a stochastic unit cell representing the random heterogeneous materials. Then this stochastic unit cell can be used to obtain the upper bound and lower bound of efiective properties using VAMUCH (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 efiective properties of a deterministic unit cell with decreasing randomness of the stochastic unit cell. To illustrate the application of this method, various examples are analyzed and compared with other theories.