Maxwell Homogenization Scheme in Micromechanics: an Overview

Abstract

The paper discuss the classical Maxwell’s (1873) homogenization method and the problems appearing in its practical implications. The method equates the far fields produced by a set of inhomogeneities and by a fictitious domain with unknown effective properties. It is re-written in terms of the property contribution tensors. The shape of the effective inclusion substantially affects the overall elastic properties. The choice of this shape in the case of anisotropic composite is a non-trivial problem. Another problem is related to the possible appearance of artificial singularities in the process of homogenization. We illustrate the method by several examples.