Electromagnetic homogenization of particulate composite materials comprising spheroids and truncated spheroids with orientational distribution

Implementations of the Bruggeman and Maxwell Garnett homogenization formalisms were developed to estimate the relative permittivity dyadic of a homogenized composite material (HCM), namely $\underline{\underline{\epsilon}}^{\rm HCM}$, arising from randomly distributed mixtures of electrically-small particles with spheroidal shapes and truncated spheroidal shapes. The two/three-dimensional (2D/3D) orientational distributions of the component particles were specified by a Gaussian probability density function. Numerical investigations were undertaken to explore the relationship between the anisotropy of the HCM and the standard deviation of the orientational distribution. For 2D distributions of orientation, $\underline{\underline{\epsilon}}^{\rm HCM}$ is generally biaxial but it becomes uniaxial when the standard deviation approaches zero or exceeds 3. For 3D distributions of orientation, $\underline{\underline{\epsilon}}^{\rm HCM}$ is generally uniaxial; however, it becomes isotropic when the standard deviation exceeds unity, with greater degrees of HCM anisotropy arising at smaller values of standard deviation. The estimates of $\underline{\underline{\epsilon}}^{\rm HCM}$ delivered by the Bruggeman formalism and the Maxwell Garnett formalism are in broad agreement, over much of the volume-fraction range appropriate to the Maxwell Garnett formalism, but the degree of HCM anisotropy predicted by the Maxwell Garnett formalism is generally a little higher than that predicted by the Bruggeman formalism, especially at low values of standard deviation.