OPTIMAL LOWER BOUNDS ON THE ELASTIC ENERGY OF A COMPOSITE MADE FROM 2 NON-WELL-ORDERED ISOTROPIC MATERIALS

This paper is a continuation of our previous work [AK] concerning optimal bounds on the effective behavior of a mixture of two linearly elastic materials. While in [AK] we restricted our attention to the case of two well-ordered components, here we focus on the case of two non-well-ordered and isotropic ones, i.e., the case when the smaller shear and bulk moduli do not belong to the same material. For given volume fractions and average strain, we establish an optimal lower bound on the effective energy quadratic form. We give two proofs of this result: one based on the Hashin-Shtrikman-Walpole variational principle, the other on the translation method.