Anisotropic homogenized composite mediums arising from truncated spheres, spheroids, and ellipsoids

TL;DR

This paper derives closed-form depolarization dyadics for truncated spheroids and ellipsoids, and applies Maxwell Garnett formalism to relate inclusion shape to anisotropy in composite mediums.

Contribution

It extends the formalism to truncated ellipsoids and develops a homogenization method linking inclusion geometry to medium anisotropy.

Findings

Anisotropy increases with deviation from spherical shape.

Closed-form expressions enable accurate modeling of composite mediums.

The formalism applies to various truncated geometries.

Abstract

Closed-form expressions were recently derived for depolarization dyadics for truncated spheres and truncated spheroids, and the formalism was extended to truncated ellipsoids. These results were exploited to develop an implementation of the Maxwell Garnett homogenization formalism for the relative permittivity parameters of homogenized composite mediums (HCMs) arising from an isotropic host medium impregnated with isotropic inclusions that are truncated spheres, spheroids, and ellipsoids. In so doing, the anisotropy of the HCM was related to the geometry of the inclusions: in general, the more the shape of the inclusions deviated from spherical, the greater was the degree of anisotropy exhibited by the HCM.