Bruggeman homogenization of a particulate composite material comprising truncated spheres and spheroids

Abstract

Closed-form expressions were established for depolarization dyadics for a truncated sphere and a truncated spheroid, both electrically small, immersed in a uniaxial dielectric ambient medium. These depolarization dyadics were used to develop the Bruggeman homogenization formalism to predict the relative permittivity dyadic of a homogenized composite material (HCM) arising from a randomly distributed mixture of oriented particles shaped as truncated spheres and spheroids. Unlike other homogenization formalisms, most notably the Maxwell Garnett formalism, the Bruggeman formalism is not restricted to composites containing dilute volume fractions of constituent particles. Numerical investigations highlighted the anisotropy of the HCM and its relation to the shapes of the constituent particles and their volume fractions. Specifically, greater degrees of HCM anisotropy arise from constituent particles whose shapes deviate more from spherical, especially for mid-range volume fractions.