Variational bounds on the effective moduli of anisotropic composites

Graeme W. Milton, Robert Kohn

Research output: Contribution to journalArticle

Abstract

The vritional inequalities of Hashin and Shtrikman are transformed to a simple and concise form. They are used to bound the effective conductivity tensor σ* of an anisotropic composite made from an arbitrary number of possibly anisotropic phases, and to bound the effective elasticity tensor C* of an anisotropic mixture of two well-ordered isotropic materials. The bounds depend on the conductivities and elastic moduli of the components and their respective volume fractions. When the components are isotropic the conductivity bounds, which constrain the eigenvalues of σ*, include those previously obtained by Hashin and Shtrikman, Murat and Tartar, and Lurie and Cherkaev. Our approach can also be used in the context of linear elasticity to derive bounds on C* for composites comprised of an arbitrary number of anisotropic phases. For two-component composites our bounds are tighter than those obtained by Kantor and Bergman and by Francfort and Murat, and are attained by sequentially layered laminate materials.

Original languageEnglish (US)
Pages (from-to)597-629
Number of pages33
JournalJournal of the Mechanics and Physics of Solids
Volume36
Issue number6
DOIs
StatePublished - 1988

Fingerprint

conductivity
Tensors
composite materials
Elasticity
Composite materials
elastic properties
tensors
laminates
Laminates
Volume fraction
modulus of elasticity
eigenvalues
Elastic moduli

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

Variational bounds on the effective moduli of anisotropic composites. / Milton, Graeme W.; Kohn, Robert.

In: Journal of the Mechanics and Physics of Solids, Vol. 36, No. 6, 1988, p. 597-629.

Research output: Contribution to journalArticle

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