Hashin-Shtrikman Bounds for Multiphase Composites

Liping Liu
California Institute of Technology

Abstract: This paper addresses the attainability of the Hashin-Shtrikman bounds for multiphase composites, including those of conductive materials and elastic materials. It presents a new derivation of these bounds that yield a necessary and sufficient condition for optimal microstructures. A key idea is a simple characterization of the gradient Young measures associated with optimal microstructures.

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