Pp. Castaneda, EXACT 2ND-ORDER ESTIMATES FOR THE EFFECTIVE MECHANICAL-PROPERTIES OF NONLINEAR COMPOSITE-MATERIALS, Journal of the mechanics and physics of solids, 44(6), 1996, pp. 827-862
Motivated by previous small-contrast perturbation estimates, this pape
r proposes a new method for estimating the effective behavior of nonli
near composite materials with arbitrary phase contrast. The key idea i
s to write down a second-order Taylor expansion for the phase potentia
ls, about appropriately defined phase average strains. The resulting e
stimates, which are exact to second order in the contrast, involve the
''tangent'' modulus tensors of the nonlinear phase potentials, and re
duce the problem for the nonlinear composite to a linear problem for a
n anisotropic thermoelastic composite. Making use of a well-known resu
lt by Levin for two-phase thermoelastic composites, together with esti
mates of the Hashin-Shtrikman type for linear elastic composites, expl
icit results are generated for two-phase nonlinear composites with sta
tistically isotropic particulate microstructures. Like the earlier sma
ll-contrast asymptotic results, the new estimates are found to depend
on the determinant of the strain, but unlike the small-contrast result
s that diverge for shear loading conditions in the nonhardening limit,
the new estimates remain bounded and reduce to the classical lower bo
und in this limiting case. The general method is applied to composites
with power-law constitutive behavior and the results are compared wit
h available bounds and numerical estimates, as well as with other nonl
inear homogenization procedures. For the cases considered, the new est
imates are found to satisfy the restrictions imposed by the bounds, to
improve on the predictions of prior homogenization procedures and to
be in excellent agreement with the results of the numerical simulation
s. Copyright (C) 1996 Elsevier Science Ltd