An Elastic-Viscoplastic Model for Metals Subjected to High Compression

Abstract

Specific constitutive equations are proposed for a material exhibiting isotropic-elastic response in its reference configuration, strain-rate, temperature and density dependent plastic flow with isotropic and directional hardening, and thermal recovery of hardening. The shear modulus is temperature and density dependent and it vanishes when the temperature reaches the density dependent melting temperature. These equations include modifications, relative to those proposed by Rubin (1986), which are appropriate to describe metals subjected to high compression. The constitutive functions characterizing pressure are determined by comparison with a Mie-Grüneisen equation of state which includes functions that are obtained from common shock-wave experiments. To examine some of the features of these equations at high compression we consider an example of homogeneous uniaxial strain and show that the deviatoric stress may be quite large at ultra high compression rates and high compression.