Abstract of the paper ``Critique of explicit schemes for estimating
elastic properties of multiphase composites,'' with P. A. Berge
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 all of the standard approximation schemes may be easily derived.
A unified analysis of the various approximation schemes results.
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