Isotropic conductivity of two-dimensional three-component symmetric composites (original) (raw)

The effective dc-conductivity problem of isotropic, twodimensional (2D), three-component, symmetric, regular composites is considered. A simple cubic equation with one free parameter for σe(σ1, 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 behavior 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.