Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. I: the confocal ellipse construction

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 This work was done while Y. G. was a student at the Courant Institute. The work of R. V. K. was partially supported by ARO contract DAAL 03-92-G-0011 and NSF grants DMS-9404376 and DMS-9402763.