Homogenization of a random mixture of identically oriented superspheroidal particles

Depolarization dyadics were computed for superspheroidal particles made of an isotropic dielectric material and immersed in a uniaxial dielectric material. Superspheroidal shapes of two kinds were considered: one intermediate between spheroidal and cylindrical, and the other intermediate between spheroidal and cuboidal. These depolarization dyadics were employed in the Maxwell Garnett and Bruggeman homogenization formalisms to estimate the relative permittivity dyadics of homogenized composite materials (HCMs) that are random mixtures of identically oriented superspheroidal particles. The anisotropy of the HCMs was exposed through numerical investigations which revealed the dependencies of the HCM's anisotropy upon the shapes of the constituent particles and their volume fractions. The largest degrees of HCM anisotropy arose when the shape of the constituent particles deviated most from spherical, especially at mid-range volume fractions. Estimates of HCM anisotropy from the Maxwell Garnett and Bruggeman formalisms were broadly similar over the volume-fraction range appropriate for the Maxwell Garnett formalism, with modest differences being most apparent for particle shapes that deviated most from spherical.