REPRESENTATIONS FOR THE CONDUCTIVITY FUNCTIONS OF MULTICOMPONENT COMPOSITES

The effective conductivity σ* of a multicomponent composite material is considered. Integral representations for σ* treated as a holomorphic function on a polydisk with values in a half‐plane are analyzed. A representation for σ* is introduced which is symmetric in the component conductivities and for which the moments of the positive measure in the integral are directly related to the coefficients in a perturbation expansion of σ* around a homogeneous medium. This second feature, which is important for obtaining bounds on σ*, was previously available only in the two‐component case. In addition, a bound valid for any holomorphic function of the above type is proven. Copyright © 1990 Wiley Periodicals, Inc., A Wiley Company