Critique of two explicit schemes for estimating elastic properties of multiphase composites

Explicit schemes of Mori-Tanaka and Kuster-Toksoz for estimating elastic properties of multiphase composites are compared and contrasted. Both methods are known to have a limited range of validity. Reexamination of the theories and comparisons to experiment leads to the conclusion that these explicit schemes should only be used to estimate properties of systems in which the host material occupies about 70-80% or more of the total volume. By introducing the concept of a reference material, we find a mutually consistent pair of equations for effective stiffness and compliance from which many of the standard approximation schemes may be easily derived. A unified analysis of the various approximation schemes results.