Oddly Shaped Inclusions: Depolarization Dyadics and Homogenization

Closed-form expressions for depolarization dyadics were developed for truncated spheres and truncated spheroids, and the formalism was extended to truncated ellipsoids; the evaluation of depolarization dyadics for this latter case requires numerical integration. The Hölder continuity condition was exploited to fix the origin of the coordinate system for the evaluation of these depolarization dyadics. These results were used to develop an implementation of the Maxwell Garnett homogenization formalism for the relative permittivity parameters of homogenized composite mediums arising from an isotropic dielectric host medium impregnated with isotropic dielectric inclusions that are truncated spheres, spheroids, and ellipsoids. Numerical studies using this homogenization formalism illuminated the relationship between the anisotropy of the HCM and the geometry of the oddly shaped inclusions. Specifically, the HCM is anisotropic to a greater degree when the shape of the inclusions deviates more from spherical.