Eur. Phys. J. B 66, 29-35 (2008)
https://doi.org/10.1140/epjb/e2008-00382-7

Effective permittivity of materials containing graded ellipsoidal inclusions

¹ Department of Physics, University of Cagliari, Cittadella Universitaria, 09042 Monserrato (Ca), Italy
² Sardinian Laboratory for Computational Materials Science (SLACS, INFM-CNR), Cittadella Universitaria, 09042 Monserrato (Ca), Italy

Corresponding author: ^a stefano.giordano@dsf.unica.it

Received: 25 July 2008
Published online: 8 October 2008

Abstract

We prove a generic theorem stating the equivalence between a graded dielectric ellipsoid (with gradation along a family of internal confocal ellipsoids) and an anisotropic homogeneous ellipsoid. We then describe a procedure to obtain the three principal permittivities of the effective ellipsoid for any given dielectric gradation profile. Finally, we apply a multiscale approach to homogenize dispersions of ellipsoidal graded particles.