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Homogenization of spherical inclusions

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Author

Summary, in English

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.

Publishing year

2002

Language

English

Publication/Series

Technical Report LUTEDX/(TEAT-7102)/1-21/(2002)

Document type

Report

Publisher

Department of Electroscience, Lund University

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Status

Published

Report number

TEAT-7102

Research group

  • Electromagnetic theory