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

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.

Original languageEnglish (US)
Pages (from-to)933-947
Number of pages15
JournalJournal of the Mechanics and Physics of Solids
Volume43
Issue number6
DOIs
StatePublished - 1995

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ellipses
microstructure
Microstructure
composite materials
Composite materials
Structural optimization
phase transformations
energy
stiffness
Phase transitions
Stiffness
optimization

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

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