Analytical homogenization method for periodic composite materials
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Chen-2009-Analytical homogeniz.pdf
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Author(s)
Chen, Ying
Schuh, Christopher A.
Date Issued
March 2009
Journal
Physical Review B
Publisher
American Physical Society
Citation
Chen, Ying , and Christopher A. Schuh. “Analytical homogenization method for periodic composite materials.” Physical Review B 79.9 (2009): 094104. © 2009 The American Physical Society
Version
Final published version
Abstract
We present an easy-to-implement technique for determining the effective properties of composite materials with periodic microstructures, as well as the field distributions in them. Our method is based on the transformation tensor of Eshelby and the Fourier treatment of Nemat-Nasser et al. of this tensor, but relies on fewer limiting assumptions as compared to prior approaches in the literature. The final system of linear equations, with the unknowns being the Fourier coefficients for the potential, can be assembled easily without a priori knowledge of the concepts or techniques used in the derivation. The solutions to these equations are exact to a given order, and converge quickly for inclusion volume fractions up to 70%. The method is not only theoretically rigorous but also offers flexibilities for numerical evaluations.
MIT Department
Massachusetts Institute of Technology. Department of Materials Science and Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevB.79.094104
