Pp. Castaneda, 3-POINT BOUNDS AND OTHER ESTIMATES FOR STRONGLY NONLINEAR COMPOSITES, Physical review. B, Condensed matter, 57(19), 1998, pp. 12077-12083
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].