Links between effective tensors for fiber-reinforced elastic composites

Predicting the effective elasticity of a composite material based on the elasticity of the constituent materials is extremely difficult, even when the microstructure is known. In this paper we consider a link between effective elastic tensors of composites with the same microgeometry but different constituent materials. Information about the effective tensor of one composite can then be used to determine the other. The general theory of exact relations allows us to identify all such links in principle. Here we describe a special set of links, for which one of the composites can be chosen arbitrarily. Several applications are considered and a number of microstructure-independent relations satisfied by the effective elastic tensors is derived.