Anisotropic effective conductivity of materials with nonrandomly oriented inclusions of diverse ellipsoidal shapes

Effective, generally anisotropic, conductivity of a material with ellipsoidal inclusions is analyzed. The results are given in closed form. They cover, in a unified way, mixtures of inclusions of diverse eccentricities (including cracks) and arbitrary nonrandom orientational distributions. Proper parameter of inclusions concentration, in whose terms the effective conductivities are to be expressed, is identified. This parameter correctly represents contributions of the individual inclusions to the overall conductivity. It reflects inclusion shapes and is tensorial; generally, it cannot be replaced by the volume fraction parameter.