A method of homogenization of elastic media

A perturbation technique is proposed which provides a simple means of estimating the effective behavior and fluctuation fields of a heterogeneous elastic medium. The perturbation analysis is based on an integral equation which characterizes the Fourier transform of the fluctuation stress potential. The average stress tensor drives the microstructural response and is assumed given. In contrast to other perturbation methods, the first-order approximation provides a nontrivial correction to the Voigt average moduli and information concerning the strain fluctuations. The first-order term in the expansion follows from straightforward computations and incorporates the statistical information provided by two-point spatial correlations of the elastic properties. Closed form expressions are obtained for the effective moduli of a two-phase continuum with randomly distributed inclusions and the results compared against the predictions of other methods