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

Yury Grabovsky, Robert Kohn

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
Pages (from-to)933-947
Number of pages15
JournalJournal of the Mechanics and Physics of Solids
Issue number6
Publication statusPublished - 1995


ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

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