About the improvement of variational bounds for nonlinear composite dielectrics

We deal with the problem of estimating the effective properties of nonlinear composite dielectrics, specially fibrous biphasic composites in which fibers are periodically distributed following a square scheme. We present an integrated approach that combines the derivation of closed-form formulae (via the Asymptotic Homogenization Method, AHM) and bounds for the effective properties of linear composites, and a bounding procedure for the effective properties of nonlinear composites. The consistency of the AHM effective expression against the bounds is shown along with some limit cases. The improvement provided by this methodology becomes more significant in cases near percolation. Numerical results are presented.