A relation on the effective conductivity of composites

2017/07/22 by Mityushev, Vladimir
#74Q15 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1707.07143

Abstract

Consider a 2D composites with non-overlapping equal inclusions imbedded in a host material of the normalized unit conductivity. The conductivity of inclusions takes two values σ₁ and σ₂ with the probabilities p and 1-p, respectively. We prove that the effective conductivity tensor of the considered three-phase random composite is equal to the effective conductivity tensor of the two-phase deterministic composite with the same inclusions of the conductivity σ=[p(σ₁~-~σ₂)+~σ₂+σ₁σ₂] [1+σ₁-p(σ₁-σ₂)]^-1.

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