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Isotropic Conductivity of Two-Dimensional Three-Component Symmetric Composites

Leonid G. Fel·Vladimir Sh. Machavariani·David J. Bergman
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Abstract

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 $σ_{e}(σ_1,σ_2,σ_3)$ 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 behavior of $σ_{e}(σ_1,σ_2,σ_3)$ 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. Pacs: 72.15.Eb, 72.80.Tm, 61.50.Ah

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Leonid G. Fel, Vladimir Sh. Machavariani, David J. Bergman. 2000-07-03. Isotropic Conductivity of Two-Dimensional Three-Component Symmetric Composites. https://doi.org/10.1088/0305-4470%2F33%2F38%2F302

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