Advanced

Homogenization of spherical inclusions

Kristensson, Gerhard LU (2002) In Technical Report LUTEDX/(TEAT-7102)/1-22/(2002) TEAT-7102.
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:
author
organization
publishing date
type
Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7102)/1-22/(2002)
volume
TEAT-7102
pages
22 pages
publisher
[Publisher information missing]
language
English
LU publication?
yes
id
dec34bd6-f60e-4cd0-b79b-b29fcea5e74f (old id 525951)
date added to LUP
2007-09-07 10:48:36
date last changed
2016-07-06 17:17:14
@misc{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},
  language     = {eng},
  pages        = {22},
  publisher    = {ARRAY(0x7da69f0)},
  series       = {Technical Report LUTEDX/(TEAT-7102)/1-22/(2002)},
  title        = {Homogenization of spherical inclusions},
  volume       = {TEAT-7102},
  year         = {2002},
}