Optimal lower bounds on the elastic energy of a composite made from two non-well-ordered isotropic materials

Authors:
Grégoire Allaire and Robert V. Kohn

Journal:
Quart. Appl. Math. **52** (1994), 311-333

MSC:
Primary 73B27; Secondary 73K20, 73K40, 73V25

DOI:
https://doi.org/10.1090/qam/1276240

MathSciNet review:
MR1276240

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Abstract: 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.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1276240

Article copyright:
© Copyright 1994
American Mathematical Society