Effective conductivity of composites containing spheroidal inclusions: Comparison of simulations with theory

We determine, by first-passage-time simulations, the effective conductivity tensor σ_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=∞), and may be employed to model aligned, long- and short-fiber composites, anisotropic sandstones, certain laminates, and cracked media. Data for σ_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 σ_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)].