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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 HashinShtrikman (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.

The effective electrical conductivity of nonlinear laminate composites