An elastic-viscoplastic model for large deformation

Abstract

It is shown that the theory of an elastic-viscoplastic work hardening material proposed by Bodner and Partom for small deformations may be generalized for large deformations by reformulating the equations using Lagrangian quantities. Restrictions on the general constitutive equations were obtained using the thermodynamic procedures proposed by Green and Naghdi. In this formulation the stress is determined directly from deformation quantities and in particular is not calculated using a hypoelastic type equation for a stress rate. Also, since Lagrangian quantities are used there is no need to introduce special rates like the Jaumann rate in the evolution equations. Specific constitutive equations were proposed for a material exhibiting isotropic-elastic response in its reference configuration, strain-rate and temperature dependent plastic flow with isotropic and directional hardening, and thermal recovery of hardening. These specific equations use only the material constants obtained from the corresponding small deformation theory. Examples of simple tension and simple shear show that these equations predict physically plausible material response for large deformations.