The extension of the Maxwell Garnett mixing rule for dielectric composites with nonuniform orientation of ellipsoidal inclusions

Abstract

This paper presents the extension of the Maxwell Garnett effective medium model accounting for an arbitrary orientation of ellipsoidal inclusions. The proposed model is shown to be asymptotically convergent to the Maxwell Garnett mixing rule for a homogenous distribution of inclusions. Subsequently, a special case of a thin composite layer with a two-dimensional distribution of inclusions is considered and a simplified Maxwell Garnett formula is formally derived. The proposed model is validated against the alternative theoretical calculations and measurements data.