Generalization of Maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape

The paper focuses on the reformulation of classical Maxwell’s (1873) homogenization method for elastic composites. Maxwell’s scheme that equates the far fields produced by a set of inhomogeneities and by a fictitious domain with unknown effective properties is re-written in terms of the compliance contribution tensors. Explicit formula for tensor of effective elastic compliances is derived for the case the ellipsoidal fictitious domain. The method is illustrated by four examples – material containing multiple identical spheroidal pores, material containing three families of inhomogeneities having different shapes and properties, material containing circular cracks that have preferential orientation with certain scatter, and material containing randomly oriented non-ellipsoidal (superspherical) pores.