Abstract
A question that has often been raised is: “How accurate is the effective medium approximation?” The question is significant in view of the fact that different effective medium theories, derived with the same goal of describing a “random” composite, can produce drastically different predictions. In the first part of this paper I illustrate with several examples that different versions of effective medium theories are actually associated with different underlying microstructures. This fact explains a major part of the discrepancies in the predictions of various effective medium theories. The recognition of the role of microstructure naturally raises to the forefront the need for a general and precise method for incorporating structural information in the calculation of electric and elastic properties of composites. The second half of the paper addresses part of this problem by presenting a first-principle approach to the calculation of effective elastic moduli for arbitrary periodic composites. By using Fourier coefficients of the periodic system as structural inputs, the new method offers the advantage of circumventing the need for explicit boundary-conditions matching across material interfaces. As a result, it can handle complex unit cell geometries just as easily as simple cell geometries.
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References
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© 1986 Springer-Verlag New York Inc.
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Sheng, P. (1986). Microstructures and Physical Properties of Composites. In: Ericksen, J.L., Kinderlehrer, D., Kohn, R., Lions, JL. (eds) Homogenization and Effective Moduli of Materials and Media. The IMA Volumes in Mathematics and its Applications, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8646-9_10
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DOI: https://doi.org/10.1007/978-1-4613-8646-9_10
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