Homogenization of spherical inclusions
(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:
http://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)/1-22/(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
@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 = {[Publisher information missing]}, language = {eng}, pages = {22}, series = {Technical Report LUTEDX/(TEAT-7102)/1-22/(2002)}, title = {Homogenization of spherical inclusions}, volume = {TEAT-7102}, year = {2002}, }