The nearly isotropic behaviour of high-rank nonlinear sequentially laminated composites

The effective transport behaviour, in the context of electrical conductivity, of sequentially laminated composites with nonlinear behaviour of the constituents is considered. An expression for the effective electric potential of two-dimensional composites is developed from the classical variational principle. This provides the means for determining the effective potential of a rank-N sequentially laminated composite with arbitrary volume fractions and lamination directions of the core laminates, in terms of an N-dimensional optimization problem. The effective potentials of sequentially laminated composites with power-law behaviour of the constituent phases are determined. It is demonstrated that the behaviour of sufficiently high-rank sequentially laminated composites tends to be isotropic. Two families of composites with both resistive and conductive inclusions are considered. The overall behaviour of these composites is compared with corresponding available bounds and estimates. It is found that the behaviours of composites belonging to these two families are, respectively, more conductive and more resistive than the corresponding second-order estimates of Ponte Castañeda and Kailasam.