EFFECTIVE CONDUCTIVITY OF COMPOSITES CONTAINING SPHEROIDAL INCLUSIONS - COMPARISON OF SIMULATIONS WITH THEORY

We determine, by first-passage-time simulations, the effective conductivity tensor sigma(e) of anisotropic suspensions of aligned spheroidal inclusions with aspect ratio b/a. This is a versatile model of composite media, containing the special limiting cases of aligned disks (b/a = 0), spheres (b/a = 1), and aligned needles (b/a = infinity), and may be employed to model aligned, long- and short-fiber composites, anisotropic sandstones, certain laminates, and cracked media. Data for sigma(e) are obtained for prolate cases (b/a = 2, 5, and 10) and oblate cases (b/a = 0.1, 0.2, and 0.5) over a wide range of inclusion volume fractions and selected phase conductivities (including superconducting inclusions and perfectly insulating ''voids''). The data always lie within second-order rigorous bounds on sigma(e) due to Willis [J. Mech. Phys. Solids 25, 185 (1977)] for this model. We compare our data for prolate and oblate spheroids to our previously obtained data for spheres [J. Appl. Phys. 69, 2280 (1991)].