Abstract
A two−phase material in which the phase boundaries are cylindrical surfaces is considered. The generators of the phase boundaries are parallel to the z axis and the x and y axes are the principal axes of the effective conductivity tensor. If the two phases have conductivities σ1 and σ2, then the effective conductivity σx* (σ1,σ2) (in the x direction) of the material and the effective conductivity σy* (σ2,σ1) (in the y direction) of the material obtained by interchanging the two phases are related by σx* (σ1,σ2) σy* (σ2,σ1) =σ1,σ2. For a statistically isotropic material σx* (σ1,σ2) =σy* (σ1,σ2) =σ* (σ1,σ2). If, in addition, the material is statistically symmetric so that interchange of the two phases yields again the same material, then σ* (σ1,σ2) =σ* (σ2,σ1) = (σ1σ2)1/2.
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