BOUNDS ON THE CONDUCTIVITY OF A RANDOM ARRAY OF CYLINDERS

The authors consider the problem of determining rigorous third-order and fourth-order bounds on the effective conductivity of sigma //2 randomly distributed throughout a matrix of conductivity sigma //1. Both bounds involve the microstructural parameter zeta //2 which is an integral that depends upon S//3, the three-point probability function of the composite. The key multidimensional integral zeta //2 is greatly simplified by expanding the orientation-dependent terms of its integrand in Chebyshev polynomials and using the orthogonality properties of this basis set.