Bruggeman formalism vs. `Bruggeman formalism': Particulate composite materials comprising oriented ellipsoidal particles

TL;DR

This paper compares two Bruggeman formalisms for homogenizing composite materials with oriented ellipsoidal particles, highlighting differences that depend on particle shape, volume fraction, and material dissipation.

Contribution

It clarifies which Bruggeman formalism correctly uses polarizability dyadics, resolving confusion in homogenization methods for anisotropic composites.

Findings

Numerical differences are significant for aspherical particles.

Discrepancies increase at mid-range volume fractions.

Correct formalism accounts for particle polarizability accurately.

Abstract

Two different formalisms for the homogenization of composite materials containing oriented ellipsoidal particles of isotropic dielectric materials are being named after Bruggeman. Numerical studies reveal clear differences between the two formalisms which may be exacerbated: (i) if the component particles become more aspherical, (ii) at mid-range values of the volume fractions, and (iii) if the homogenized component material is dissipative. The correct Bruggeman formalism uses the correct polarizability density dyadics of the component particles, but the other formalism does not.