HOMOGENEITY IN INTEGRAL-REPRESENTATIONS FOR EFFECTIVE PROPERTIES OF COMPOSITE-MATERIALS

The effective complex conductivity sigma of an n-component composite material is considered. Recently; an integral representation that trea ts the component conductivities sigma(1),...,sigma(n) symmetrically wa s developed. This representation has the advantage that the moments of the positive measure in the integral are directly related to the coef ficients in a perturbation expansion of sigma around a homogeneous me dium. However, the admissible class of measures has been difficult to characterize, due to the condition that sigma is a homogeneous functi on of the component conductivities. Here, this admissible class is cha racterized in terms of linear relations among the moments associated w ith tetrahedra in Fourier space Z(n). The homogeneity is used to deriv e a new formula for sigma in the two-component case, in which sigma* for general media is expressed in terms of the conductivities of lamin ates of second rank. (C) 1995 American Institute of Physics.