Monday, 11 October 2004 - 1:50 PM

This presentation is part of : Torquato Symposium

Macroscopic behavior and field fluctuations in nonlinear composites

Pedro Ponte Castaneda, Ecole Polytechnique, Departement de Mecanique, Palaiseau, 91128, France and Martin Idiart, University of Pennsylvania, 220 S. St., MEAM, Philadelphia, PA 19104-6315.

This paper deals with a second-order theory for estimating the effective behavior of strongly nonlinear composites. The new theory makes use of the field fluctuations in the phases of the relevant “linear comparison composite” to generate improved Hashin-Shtrikman (HS) and self-consistent (SC) types of approximations for nonlinear media. The resulting HS and SC predictions are exact to second-order in the contrast, and satisfy all known bounds. In particular, the new SC estimates exhibit a nonlinearity-independent percolation threshold, and critical exponents that are consistent with recently developed bounds on these exponents. In addition, the new theory can be used to obtain predictions for the covariance tensor of the field fluctuations in the phases of the nonlinear composite. The results for the overall behavior, as well as for the field fluctuations will be compared to the results of recent numerical simulations.

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