A complete characterization of the possible bulk and shear moduli of planar polycrystals

M. Avellaneda, A. V. Cherkaev, L. V. Gibiansky, G. W. Milton, M. Rudelson

Research output: Contribution to journalArticlepeer-review


This paper investigates the range of possible elastic moduli of two-dimensional isotropic polycrystals. The polycrystals are comprised of grains obtained from a single orthotropic material. The overall elastic properties are described by an effective bulk modulus Κ0 and an effective shear modulus μ0. The pair (Κ0, μ0) is shown to be confined to a rectangle in the (Κ, μ) plane. Microstructures are identified which correspond to every point within the rectangle, and in particular to the corner points. Optimal bounds on the effective Poisson's ratio and Young's modulus follow immediately. Under a certain constraint on the crystal moduli, the rectangle degenerates to a line segment: the effective shear modulus of such a polycrystal is microstructure independent. This extends earlier work that established microstructure independence for polycrystals constructed from square symmetric crystals.

Original languageEnglish (US)
Pages (from-to)1179-1218
Number of pages40
JournalJournal of the Mechanics and Physics of Solids
Issue number7
StatePublished - Jul 1996

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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