Quarterly of Applied Mathematics

Suh, J.K., Li A., Woo, S.L-Y.


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 1inear 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.