Conductivity tensor of anisotropic composite media from the microstructure

S. Torquato, Asok K. Sen

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

Perturbation expansions and rigorous bounds on the effective conductivity tensor σe of d-dimensional anisotropic two-phase composite media of arbitrary topology have recently been shown by the authors to depend upon the set of n-point probability functions S(i)1,., S(i)n. S(i)n gives the probability of simultaneously finding n points in phase i (i=1,2). Here we describe a means of representing these statistical quantities for distributions of identical, oriented inclusions of arbitrary shape. Our results are applied by computing second-order perturbation expansions and bounds for a certain distribution of oriented cylinders with a finite aspect ratio. We examine both cases of conducting cylindrical inclusions in an insulating matrix and of insulating cracks or voids in a conducting matrix.

Original languageEnglish (US)
Pages (from-to)1145-1155
Number of pages11
JournalJournal of Applied Physics
Volume67
Issue number3
DOIs
StatePublished - 1990

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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