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Effective conductivity and average polarizability of random polycrystals

Avellaneda, Marco and Bruno, Oscar (1990) Effective conductivity and average polarizability of random polycrystals. Journal of Mathematical Physics, 31 (8). pp. 2047-2056. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:AVEjmp90

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Abstract

A third-order expansion for the effective thermal conductivity tensor κ* of anisotropic polycrystalline cell materials is derived. The coefficients of the expansion are given in terms of the average polarizability tensor, a nondimensional quantity determined from the grain shape and crystallographic orientation distributions independent of other details of the microgeometry such as two (or more) particle correlation functions. Explicit numerical results for a wide variety of microgeometries made of ellipsoidal cells are obtained. This calculation uses a new method that exploits the symmetry properties of the effective conductivity tensor of a cell material as a function of the single-crystal conductivities.


Item Type:Article
Additional Information:Copyright © 1990 American Institute of Physics. (Received 2 October 1989; accepted 28 March 1990) We are grateful to Professor G. Milton and Dr. J. Berryman for useful discussion which helped improve this paper. This research was partially supported by a National Science Foundation Grant No. NSF-DMS-8802739 and by the US Army Research Office through Grant Nos. ARO-DAAL-0389K0039 and ARO-DAAL-0388K0110.
Subject Keywords:POLYCRYSTALS; RANDOMNESS; THERMAL CONDUCTIVITY; SERIES EXPANSION; TENSORS; ANISOTROPY; POLARIZABILITY; VECTORS; CRYSTAL ORIENTATION; DISTRIBUTION; NUMERICAL DATA; CORRELATION FUNCTIONS; CALCULATION METHODS; SYMMETRY
Record Number:CaltechAUTHORS:AVEjmp90
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:AVEjmp90
Alternative URL:http://dx.doi.org/10.1063/1.528656
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9059
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:24 Oct 2007
Last Modified:26 Dec 2012 09:45

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