Second-order estimates for nonlinear isotropic composites with spherical voids and rigid particles

M. I. IDIART; P. PONTE CASTAÑEDA

Comptes Rendus Mecanique

Elsevier

Año: 2005 vol. 333 p. 147 - 154

1631-0721

The ``second-order'' nonlinear homogenization method (Ponte Casta\~neda, J. Mech. Phys. Solids 50 (2002) 737--757) is used to generate estimates of the Hashin-Shtrikman-type for the effective behavior of viscoplastic materials with isotropically distributed spherical pores or rigid particles. In the limiting case of an ideally plastic matrix with a dilute concentration of pores, the resulting estimates were found to exhibit a linear dependence on the porosity when the material is subjected to axisymmetric shear, but this dependece becomes singular for simple shear. In the process of this work, an alternative prescription for certain reference tensors used in the method is proposed, and shown to lead to more consistent estimates for the effective behavior than the earlier prescription.