Effective conductivities of heterogeneous media containing multiple inclusions with various spatial distributions

Duan, H. L., Karihaloo, Bhushan Lal ORCID: https://orcid.org/0000-0003-0657-2678, Wang, J. and Yi, X. 2006. Effective conductivities of heterogeneous media containing multiple inclusions with various spatial distributions. Physical Review B: Condensed Matter and Materials Physics 73 (17) , 174203. 10.1103/PhysRevB.73.174203

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Abstract

A scheme is proposed for predicting the effective conductivities of heterogeneous media containing ellipsoidal inclusions of diverse shapes, spatial distributions, and orientations. This scheme yields explicit expressions for the effective conductivity tensor in terms of three microstructural parameters that characterize the shape, distribution, and orientation of the inclusions. By expanding the effective conductivity tensor in terms of the volume fraction of the inclusions, it is found that the effect of the shape of the distribution ellipsoid on the effective conductivity tensor is of a higher order in the volume fraction than the effect of the shape of the inclusions. The scheme proposed here generalizes the Maxwell formula to heterogeneous media containing multiple inclusions while also taking into account the orientation of the inclusions. Thus, the existing formulas in the literature are special cases of the general formulas given by the present scheme. The predicted effective conductivities of heterogeneous media containing aligned ellipsoidal inclusions, randomly oriented ellipsoidal inclusions, spheroidal inclusions with orientational distributions, and mixtures of cavities and cracks are found to agree well with the experimental results and the results of other schemes.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Publisher:	American Physical Society
ISSN:	1098-0121
Last Modified:	05 May 2023 18:38
URI:	https://orca.cardiff.ac.uk/id/eprint/13623

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