Homogenization of spherical inclusions

被引：13

作者：

Kristensson, G. ^{[1
]}

机构：

[1] Department of Electroscience, Electromagnetic Theory, Lund Institute of Technology, SE-221 00 Lund

来源：

Progress in Electromagnetics Research | 2003年 / 42卷

关键词：

Functional behaviors - Heterogeneous materials - Higher order terms - Maxwell-Garnett formula - Relative permittivity - Series representations - Spherical coordinates - Spherical inclusion;

D O I：

10.2528/PIER03012702

中图分类号：

学科分类号：

摘要：

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.

引用

页码：1 / 25

页数：24

共 19 条

[1]

Allaire G., Homogenization and two-scale convergence, SIAM J. Math. Anal., 23, 6, pp. 1482-1518, (1992)

[2]

Bossavit A., On the homogenization of Maxwell equations, COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 14, 4, pp. 23-26, (1995)

[3]

Bostrom A., Kristensson G., Strom S., Transformation properties of plane, spherical and cylindrical scalar and vector wave functions, Field Representations and Introduction to Scattering, pp. 165-210, (1991)

[4]

Cioranescu D., Donato P., An Introduction to Homogenization, (1999)

[5]

Doyle W.T., The Clausius-Mossotti problem for cubic array of spheres, J. Appl. Phys., 49, 2, pp. 795-797, (1978)

[6]

Edmonds A.R., Angular Momentum in Quantum Mechanics, (1960)

[7]

Jikov V.V., Kozlov S.M., Oleinik O.A., Homogenization of Differential Operators and Integral Functionals, (1994)

[8]

Lam J., Magnetic permeability of a simple cubic lattice of conducting magnetic spheres, J. Appl. Phys., 60, 12, pp. 4230-4235, (1986)

[9]

McKenzie D.R., McPhedran R.C., Derrick G.H., The conductivity of lattices of spheres. II. The body centred and face centred cubic lattices, Proc. Roy. Soc. London, A362, pp. 211-232, (1978)

[10]

McPhedran R.C., McKenzie D.R., The conductivity of lattices of spheres. I. The simple cubic lattice, Proc. Roy. Soc. London, A359, pp. 45-63, (1978)

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