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Inverse bounds and bulk properties of complex-valued two-component composites

Engström, Christian LU (2006) In SIAM Journal on Applied Mathematics 67(1). p.194-213
Abstract
The bulk properties of composites are known to depend strongly on the microstructure. This dependence can be quantified in terms of a representation introduced by D. Bergman, which factorizes the geometry dependence from the contrast. Based on this analytic representation of the effective permittivity, we present a general scheme to estimate the microstructural parameters such as the volume fraction and the anisotropy of two-component composites. The estimates are given as bounds, that is, the largest parameter region which is compatible with the available information. Thus, more information produces better estimates on the microstructural parameters. The method, which uses complex-valued measurements of bulk properties of the composite,... (More)
The bulk properties of composites are known to depend strongly on the microstructure. This dependence can be quantified in terms of a representation introduced by D. Bergman, which factorizes the geometry dependence from the contrast. Based on this analytic representation of the effective permittivity, we present a general scheme to estimate the microstructural parameters such as the volume fraction and the anisotropy of two-component composites. The estimates are given as bounds, that is, the largest parameter region which is compatible with the available information. Thus, more information produces better estimates on the microstructural parameters. The method, which uses complex-valued measurements of bulk properties of the composite, is illustrated by numerical examples. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Pade approximations, Stieltjes integral, inverse homogenization, composite, inverse bounds
in
SIAM Journal on Applied Mathematics
volume
67
issue
1
pages
194 - 213
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • wos:000243279300009
  • scopus:33847699287
ISSN
0036-1399
DOI
10.1137/060649598
language
English
LU publication?
yes
id
8415ef3a-4859-48aa-bd20-8618911fcfd4 (old id 677634)
date added to LUP
2016-04-01 16:15:27
date last changed
2021-02-17 06:38:22
@article{8415ef3a-4859-48aa-bd20-8618911fcfd4,
  abstract     = {The bulk properties of composites are known to depend strongly on the microstructure. This dependence can be quantified in terms of a representation introduced by D. Bergman, which factorizes the geometry dependence from the contrast. Based on this analytic representation of the effective permittivity, we present a general scheme to estimate the microstructural parameters such as the volume fraction and the anisotropy of two-component composites. The estimates are given as bounds, that is, the largest parameter region which is compatible with the available information. Thus, more information produces better estimates on the microstructural parameters. The method, which uses complex-valued measurements of bulk properties of the composite, is illustrated by numerical examples.},
  author       = {Engström, Christian},
  issn         = {0036-1399},
  language     = {eng},
  number       = {1},
  pages        = {194--213},
  publisher    = {Society for Industrial and Applied Mathematics},
  series       = {SIAM Journal on Applied Mathematics},
  title        = {Inverse bounds and bulk properties of complex-valued two-component composites},
  url          = {http://dx.doi.org/10.1137/060649598},
  doi          = {10.1137/060649598},
  volume       = {67},
  year         = {2006},
}