Asymptotics of the effective conductivity of composites with closely spaced inclusions of optimal shape

Y. Gorb, L. Berlyand

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We consider a mathematical model of a high contrast two phase composite material with inclusions (fibres) close to touching in two space dimensions. The inclusions form a periodic array and have an optimal shape which is a curvilinear square with rounded-off angles ('nearly square' shape) described by a flattening parameter m. We derive an asymptotic formula for the effective conductivity Âδ of the composite when the interparticle distance δ goes to zero. This formula captures the dependence of Âδ on the parameter m. We provide a rigorous justification for this asymptotic formula by a variational duality approach.

Original languageEnglish (US)
Pages (from-to)83-106
Number of pages24
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume58
Issue number1
DOIs
StatePublished - Feb 1 2005

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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