Microstructures of Composites of Extremal Rigidity and Exact Bounds on the Associated Energy Density
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We study the elastic composites of extremal stiffness, i.e., periodic structures that provide minimal energy density in a given stress field (we call them composites of the minimal compliance or of the maximal stiffness). The composites are assembled from two isotropic materials taken in a prescribed proportion, and may be of an arbitrary microstructure.
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