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Exact Results for Conductivity of 2D Isotropic Heterophase Systems

S. A. Bulgadaev
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Abstract

The duality relation for the effective conductivity sigma_{e} of 2D isotropic heterophase systems is used for obtaining the exact results for sigma_{e} at arbitrary number of phases N. The exact values of sigma_{e} correspond to the fixed points of the duality transformations. The new exact results for sigma_{e}, generalizing the well-known exact values of sigma_{e} for N = 2,3 at equal phase concentrations, are found. It is shown that for N > 3 there exist the whole hyperplanes in the space of phase concentrations, on which sigma_{e} takes constant values. These results are checked in the framework of various approximations for different random heterophase systems.

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S. A. Bulgadaev. 2003-06-01. Exact Results for Conductivity of 2D Isotropic Heterophase Systems. https://doi.org/10.1016/s0375-9601(03)00729-1

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