### Homogenization of spherical inclusions

(2002) In Technical Report LUTEDX/(TEAT-7102)/1-21/(2002)- Abstract
- 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... (More) - 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. (Less)

Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/525951

- author
- Kristensson, Gerhard
^{LU} - organization
- publishing date
- 2002
- type
- Book/Report
- publication status
- published
- subject
- in
- Technical Report LUTEDX/(TEAT-7102)/1-21/(2002)
- pages
- 22 pages
- publisher
- Department of Electroscience, Lund University
- report number
- TEAT-7102
- language
- English
- LU publication?
- yes
- additional info
- Published version: Electromagnetic Waves PIER 42, Ed. J.A. Kong, pp. 1-25, EMW Publishing, Cambridge, Massachusetts, USA, 2003.
- id
- dec34bd6-f60e-4cd0-b79b-b29fcea5e74f (old id 525951)
- date added to LUP
- 2016-04-04 13:48:02
- date last changed
- 2020-09-09 14:10:15

@techreport{dec34bd6-f60e-4cd0-b79b-b29fcea5e74f, abstract = {{The homogenization of cubically arranged, homogeneous spherical inclusions<br/><br> in a background material is addressed. This is accomplished by the solution of<br/><br> a local problem in the unit cell. An exact series representation of the eﬀective<br/><br> relative permittivity of the heterogeneous material is derived, and the functional<br/><br> behavior for small radii of the spheres is given. The solution is utilizing<br/><br> the translation properties of the solutions to the Laplace equation in spherical<br/><br> coordinates. A comparison with the classical mixture formulas, e.g., the<br/><br> Maxwell Garnett formula, the Bruggeman formula, and the Rayleigh formula,<br/><br> shows that all classical mixture formulas are correct to the ﬁrst (dipole) order,<br/><br> and, moreover, that the Maxwell Garnett formula predicts several higher order<br/><br> terms correctly. The solution is in agreement with the Hashin-Shtrikman<br/><br> limits.}}, author = {{Kristensson, Gerhard}}, institution = {{Department of Electroscience, Lund University}}, language = {{eng}}, number = {{TEAT-7102}}, series = {{Technical Report LUTEDX/(TEAT-7102)/1-21/(2002)}}, title = {{Homogenization of spherical inclusions}}, url = {{https://lup.lub.lu.se/search/files/83467154/TEAT_7102.pdf}}, year = {{2002}}, }