EXACT 2ND-ORDER ESTIMATES OF THE SELF-CONSISTENT TYPE FOR NONLINEAR COMPOSITE-MATERIALS

This work is concerned with the application of a general procedure for estimating the effective behavior of nonlinear composites to obtain n ew estimates of the self-consistent type. The procedure makes use of a linear comparison thermoelastic composite with the tangent moduli of the nonlinear phases, evaluated at appropriately chosen estimates for the average strain in the phases. Unlike the classical incremental and secant modulus self-consistent estimates for nonlinear composites, th e new self-consistent estimates are found to satisfy all known bounds, including some recently established bounds of the Hashin-Shtrikman ty pe. Also, the new self-consistent estimates are found to be exact to s econd order in the contrast, and thus, in agreement with recently esta blished small-contrast asymptotic expansions for nonlinear composites. In addition, for composites with incompressible, isotropic phases and statistically isotropic microstructures, the new self-consistent esti mates are found to depend on the determinant of the strain, thus givin g different predictions under uniaxial and simple shear loading condit ions. (C) 1998 Elsevier Science Ltd. All rights reserved.