[1] [1] () [1] [1] [1] [1] [1]   [1]   [1]   [1]   [1]   et al. [1] Proof:   Remark:  

$$\begin{eqnarray} { \enq{\end{eqnarray}$$ (1)

x x a b c d e E g h j J m n p ^ q r ^ s t u v w x . y z ^ ^ ^ ^ ^ 1_n 1_m A B C D F G H I J k K L M N O 0 P Q R S T T U V W X Y Z R 0&^T&0 &00& A C D E F G K L P R

S T V W min max LS [1]LS[#1] [1]LS[#1] Int Bdy k_- k_+ k_s i(r - t) i(r - t) i(z - t)

Explicit schemes for estimating elastic properties of multiphase composites

James G. Berryman

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ABSTRACT

Explicit schemes of Mori-Tanaka and Kuster-Toksöz 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 lead to the conclusion that these explicit schemes should not be used to estimate properties of systems in which the host material occupies less than $50\%$ of the total volume. A unified approach to derivation of these explicit methods, as well as some implicit methods, is also presented.