Constitutive Restrictions for Idealized Elastic-Viscoplastic Materials

This paper is concerned mainly with restrictions on constitutive equations of idealized elastic-viscoplastic materials in the presence of finite deformation. The development is confined to the purely mechanical theory utilizing a constitutive model that includes unloading and allows for suitable definition of plastic strain. With the use of a physically plausible assumption concerning non-negative work in a closed cycle of deformation, two local inequalities are derived which place restrictions on the nonlinear constitutive response functions of the idealized material. Further implications of these inequalities relating the various response functions are dicussed. In the absence of rate effects in the stress response, the results correspond to those appropriate for rate-independent plasticity.