Inverse bounds and bulk properties of complex-valued two-component composites
(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... (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)
- author
- Engström, Christian LU
- organization
- publishing date
- 2006
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Composite, Inverse bounds, Inverse homogenization, Padé approximations, Stieltjes integral
- in
- SIAM Journal on Applied Mathematics
- volume
- 67
- issue
- 1
- pages
- 20 pages
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- scopus:33847699287
- ISSN
- 0036-1399
- DOI
- 10.1137/060649598
- language
- English
- LU publication?
- yes
- id
- 96ac9fcc-fc27-4746-967e-cbb69231892d
- date added to LUP
- 2023-03-24 11:32:15
- date last changed
- 2023-03-24 12:40:03
@article{96ac9fcc-fc27-4746-967e-cbb69231892d,
abstract = {{<p>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.</p>}},
author = {{Engström, Christian}},
issn = {{0036-1399}},
keywords = {{Composite; Inverse bounds; Inverse homogenization; Padé approximations; Stieltjes integral}},
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}},
}