Optimal bounds and microgeometries for elastic two-phase composites

Research output: Contribution to journalArticle

Abstract

Consider two isotropic, linearly elastic materials with elasticity tensors C//1, C//2 and assume C//1 less than C//2. We prove that the class of effective tensors of composites built from these materials with given volume fractions that are invariant under a given symmetry group is such that each of its elements is bounded above and below by tensors in the same class corresponding to finite-rank laminates. This implies that for any imposed uniform strain or stress field, optimal bounds on the effective strain or stress energy per unit volume are attained by finite-rank laminates. Explicit bounds on the strain energy, with no symmetry assumptions, are given in dimensions 2 and 3. These bounds are more stringent than the classical Voigt-Reuss bounds. Finally, explicit bounds and microgeometries are given for the effective moduli of composites with cubic symmetry.

Original languageEnglish (US)
Pages (from-to)1216-1228
Number of pages13
JournalSIAM Journal on Applied Mathematics
Volume47
Issue number6
StatePublished - Dec 1987

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Optimal Bound
Tensors
Tensor
Explicit Bounds
Laminates
Finite Rank
Composite
Composite materials
Symmetry
Strain Energy
Elastic Material
Stress Field
Strain energy
Symmetry Group
Volume Fraction
Elasticity
Volume fraction
Modulus
Linearly
Imply

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Optimal bounds and microgeometries for elastic two-phase composites. / Avellaneda, Marco.

In: SIAM Journal on Applied Mathematics, Vol. 47, No. 6, 12.1987, p. 1216-1228.

Research output: Contribution to journalArticle

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