In this part of the work, the Eshelby tensors of a finite spherical domain are applied to various homogenization procedures estimating the effective material properties of multiphase composites. The Eshelby tensors of a finite domain can capture the boundary effect of a representative volume element as well as the size effect of the different phases. Therefore their application to homogenization does not only improve the accuracy of classical homogenization methods, but also leads to some novel homogenization theories. This paper highlights a few of them: a refined dilute suspension method and a modified Mori–Tanaka method, the exterior eigenstrain method, the dual-eigenstrain method, which is a generalized self-consistency method, a shell model, and new variational bounds depending on the different boundary conditions. To the best of the authors’ knowledge, this is the first time that a multishell model is used to evaluate the Hashin–Shtrikman bounds for a multiple phase composite , which can distinguish some of the subtleties of different microstructures.
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July 2007
Technical Papers
The Eshelby Tensors in a Finite Spherical Domain—Part II: Applications to Homogenization
Shaofan Li,
Shaofan Li
Department of Civil and Environmental Engineering,
e-mail: li@ce.berkeley.edu
University of California
, Berkeley, CA 94720
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Gang Wang,
Gang Wang
Department of Civil and Environmental Engineering,
University of California
, Berkeley, CA 94720
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Roger A. Sauer
Roger A. Sauer
Department of Civil and Environmental Engineering,
University of California
, Berkeley, CA 94720
Search for other works by this author on:
Shaofan Li
Department of Civil and Environmental Engineering,
University of California
, Berkeley, CA 94720e-mail: li@ce.berkeley.edu
Gang Wang
Department of Civil and Environmental Engineering,
University of California
, Berkeley, CA 94720
Roger A. Sauer
Department of Civil and Environmental Engineering,
University of California
, Berkeley, CA 94720J. Appl. Mech. Jul 2007, 74(4): 784-797 (14 pages)
Published Online: June 14, 2006
Article history
Received:
April 6, 2006
Revised:
June 14, 2006
Citation
Li, S., Wang, G., and Sauer, R. A. (June 14, 2006). "The Eshelby Tensors in a Finite Spherical Domain—Part II: Applications to Homogenization." ASME. J. Appl. Mech. July 2007; 74(4): 784–797. https://doi.org/10.1115/1.2711228
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