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Microstructures minimizing the energy of a two phase elastic composite in two space dimensions.
journal contributionposted on 1994-01-01, 00:00 authored by Yury Grabovsky, Robert V. Kohn
Abstract: "For modeling coherent phase transformations and for applications to structural optimization, it is of interest to identify microstructures with minimal energy or maximal stiffness. We present a new and appealingly simple class of extremal microstructures, which we call the confocal ellipse construction, for the case of a two-dimensional elastic composite made from two isotropic elastic materials. When the macroscopic stress and strain are isotropic, our construction reduces to the well-known 'coated sphere' microstructure."