Isotropic conductivity of two-dimensional three-component symmetric composites

Leonid G. Fel, Vladimir Sh Machavariani, David J. Bergman

Research output: Contribution to journalArticlepeer-review


The effective DC conductivity problem of isotropic, two-dimensional (2D), three-component, symmetric, regular composites is considered. A simple cubic equation with one free parameter for σe1, σ2, σ3) is suggested whose solutions automatically have all the exactly known properties of that function. Numerical calculations on four different symmetric, isotropic, 2D, three-component, regular structures show a non-universal behaviour of σe, (σ1, σ2, σ3) with an essential dependence on micro-structural details, in contrast with the analogous two-component problem. The applicability of the cubic equation to these structures is discussed. An extension of that equation to the description of other types of 2D three-component structures is suggested, including the case of random structures.

Original languageEnglish
Pages (from-to)6669-6681
Number of pages13
JournalJournal of Physics A: Mathematical and General
Issue number38
StatePublished - 29 Sep 2000


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