Bounds and Self-Consistent Estimates for the Overall Properties of Nonlinear Composites

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Abstract
Variational ‘self-consistent’ estimates for nonlinear problems are formulated, building on a variational formulation previously developed by the authors. The formulation employs a linear ‘comparison medium’ for whose properties some ‘self-consistent’ choice is made. In contrast to linear problems, three possible self-consistent choices present themselves. The results that they give are analysed for two particular systems (a nonlinear dielectric and a nonlinear lossy composite) for which bounds are already available. Estimates based on self-consistent embedding of a single inclusion in a homogeneous matrix composed of ‘comparison material’ are also developed.

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