Microstructures minimizing the energy of a two phase elastic composite in two space dimensions.

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."