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Homogenization of spherical inclusions

  • J.A. Kong
Publiceringsår: 2003
Språk: Engelska
Sidor: 1-25
Publikation/Tidskrift/Serie: Progress in electromagnetics research
Volym: PIER 42
Dokumenttyp: Artikel
Förlag: Cambridge, Mass. : EMW Publishing


The homogenization of cubically arranged, homogeneous
spherical inclusions in a background material is addressed. This is
accomplished by the solution of a local problem in the unit cell.
An exact series representation of the effective relative permittivity of
the heterogeneous material is derived, and the functional behavior
for small radii of the spheres is given. The solution is utilizing
the translation properties of the solutions to the Laplace equation
in spherical coordinates. A comparison with the classical mixture
formulas, e.g., the Maxwell Garnett formula, the Bruggeman formula,
and the Rayleigh formula, shows that all classical mixture formulas
are correct to the first (dipole) order, and, moreover, that the Maxwell
Garnett formula predicts several higher order terms correctly. The
solution is in agreement with the Hashin-Shtrikman limits.



  • Technology and Engineering


  • ISSN: 1559-8985
  • ISBN: 0-9679674-5-7

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