Exact results for weakly nonlinear composites and implications for homogenization methods

Weakly nonlinear composite conductors are characterized by position-dependent dissipation potentials expressible as an additive composition of a quadratic potential and nonquadratic weighted small parameter. This form carries over to the effective when expanded first order in However, first-order correction this asymptotic expansion depends only on zeroth-order values local fields, namely, fields within perfectly linear conductor. is exploited derive exact conductivity cylinder assemblage exhibiting weak nonlinearity power-law type (i.e., power law with exponent m=1+δ, such that |δ|≪1), found be identical (to δ) corresponding result for sequentially laminated composites infinite rank. These results used assess capabilities more general homogenization methods making use properties optimally selected comparison composites.