Second-order estimates for the large-deformation response of particle-reinforced rubbers

This paper presents the application of a recently proposed 'second-order' homogenization method (J. Mech. Phys. Solids 50 (2002) 737-757) to the estimation of the effective behavior of hyperelastic composites subjected to finite deformations. The main feature of the method is the use of 'generalized' secant moduli that depend not only on the phases averages of the fields, but also on the phase covariance tensors. The use of the method is illustrated in the context of particle-, or fiber-reinforced elastomers and estimates analogous to the well-known Hashin-Shtrikman estimates for linear-elastic composites are generated. The new estimates improve on earlier estimates (J. Mech. Phys. Solids 48 (2000) 1389-1411) neglecting the use of fluctuations. In particular, the new estimates, unlike the earlier ones, are capable of recovering the exact incompressibility constraint when the matrix is also taken to be incompressible. (C) 2003 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.