New approximation for the effective energy of nonlinear conducting composites

Approximations for the effective energy and, thus, effective conductivity of nonlinear, isotropic conducting dispersions are developed. This is accomplished by using the Ponte Castaneda variational principles [Philos. Trans. R. Soc. London Ser. A 340, 1321 (1992)] and the Torquato approximation [J. Appl. Phys. 58, 3790 (1985)] of the effective conductivity of corresponding linear composites. The results are obtained for dispersions with superconducting or insulating inclusions, and, more generally, for phases with a power-law energy. It is shown that the new approximations lie within the best available rigorous upper and lower bounds on the effective energy.