Class of viscoelastoplastic constitutive models based on the maximum dissipation principle

A class of viscoelastoplastic constitutive models is derived from the maximum inelastic dissipation principle, in the framework of infinitesimal deformations, and in analogy to the elastoviscoplastic case examined in Simo and Honein. Here the existence of the equilibrium response functional with respect to which the overstress is measured, and the existence of an instantaneous elastic response are assumed. A broad set of overstress functions turns out to characterize the class of models derived herein. Both the flow rule for the viscoplastic deformation and the rate form of the constitutive equation for the class of models cited above are obtained, and the behavior of this equation under very slow strain rates and very high viscosity is investigated. A numerical simulation is also given by selecting two overstress functions available in the literature. Loading conditions of repeated strain rate variation, monotonic strain rate with relaxation and cyclic loading at different strain rates are examined, and qualitative agreement is shown with the experimental observations done in Krempl and Kallianpur and Haupt and Lion and references cited therein.