EXACT 2ND-ORDER ESTIMATES FOR THE EFFECTIVE MECHANICAL-PROPERTIES OF NONLINEAR COMPOSITE-MATERIALS

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