3-POINT BOUNDS AND OTHER ESTIMATES FOR STRONGLY NONLINEAR COMPOSITES

A variational procedure due to Ponte Castaneda et al. [Phys. Rev. B 46 , 4387 (1992)] is used to determine three-point bounds and other types of estimates for the effective response of strongly nonlinear composi tes with random microstructures. The variational procedure makes use o f estimates for the effective properties of ''linear comparison compos ites'' to generate corresponding estimates for nonlinear composites. S everal equivalent forms of the variational procedure are derived. In p articular, it is shown that the mean-held theory of Wan et al. [Phys. Rev. B 54, 3946 (1996)], which also makes use of a linear comparison c omposite, together with a certain ''decoupling approximation,'' leads to results that are precisely identical to those that can be obtained from the earlier variational procedure. Finally, three-point bounds an d other estimates are computed for power-law composites with cell-type microstructures, and the results are compared with random resistor ne twork simulations available from the literature. [S0163-1829(98)03619- 4].