Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The effective electrical conductivity of nonlinear laminate composites


Authors: Guoan Li and Andrew S. Douglas
Journal: Quart. Appl. Math. 53 (1995), 433-464
MSC: Primary 73B27; Secondary 73K20, 78A55
DOI: https://doi.org/10.1090/qam/1343461
MathSciNet review: MR1343461
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Abstract: This paper studies the effective nonlinear electrical conductivity of sequentially laminated materials in both two and three dimensions. The exact nonlinear conductive behavior is obtained through a variational procedure [1] that expresses the nonlinear properties of the laminate composite in terms of an optimization with respect to the properties of a series of linear comparison materials. Multiphase laminate composites are discussed and these results are compared with nonlinear Hashin-Shtrikman (H-S) bounds. It is found that some of the laminates possess extremal microstructures that attain the nonlinear H-S lower bound while others are very close to extremal microstructures. The results apply also to the nonlinear thermal conductivity and dielectric and magnetic behavior of laminated heterogeneous materials.


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DOI: https://doi.org/10.1090/qam/1343461
Article copyright: © Copyright 1995 American Mathematical Society


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