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The effective conductivity of strongly heterogeneous composites

Bruno, Oscar P. (1991) The effective conductivity of strongly heterogeneous composites. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 433 (1888). pp. 353-381. ISSN 1364-5021. https://resolver.caltech.edu/CaltechAUTHORS:20181106-145800580

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Abstract

We deal with the effective conductivity m = m(z) of two phase, ordered or disordered mixtures consisting of particles of material of conductivity z inserted in a matrix of conductivity 1. We focus on finding bounds on the set of values of z for which the function m is singular or vanishes, and we apply our results to the estimation of the effective conductivity of high contrast mixtures (z = 0 or z = ∞). We find that the zeroes and singularities of the function m lie on an interval of the negative real axis, which depends on the shape of the particles and the interparticle distances. Our results agree with previous numerical calculations for periodic arrays of spheres. In some cases we show that our estimates are optimal. We apply our results about the zeroes and singularities together with the complex variable method, and find bounds on the effective conductivity of matrix-particle random composites. These bounds give good estimations even in cases of high contrast, and, in many cases, they improve substantially over the bounds obtained by other methods, for the same types of high contrast mixtures.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1098/rspa.1991.0053DOIArticle
https://www.jstor.org/stable/51870JSTORArticle
ORCID:
AuthorORCID
Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 1991 The Royal Society. Received 1 October 1990; accepted 20 November 1990. We thank Professors D. Kinderlehrer, R. Kohn, G. Milton and S. Torquato for stimulating conversations on the subject of this paper. Support from ARO under contract DAAL-03-88-K-0110 is also gratefully acknowledged.
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)DAAL-03-88-K-0110
Issue or Number:1888
Record Number:CaltechAUTHORS:20181106-145800580
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181106-145800580
Official Citation:The effective conductivity of strongly heterogeneous composites. Oscar P. Bruno. Proc. R. Soc. Lond. A 1991 433 353-381; DOI: 10.1098/rspa.1991.0053. Published 8 May 1991
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90678
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Nov 2018 21:20
Last Modified:03 Oct 2019 20:27

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