A class of viscoelastoplastic constitutive models based on the maximum dissipation principle

A class of viscoelastoplastic constitutive models is derived from the maxim um inelastic dissipation principle, in the framework of infinitesimal defor mations, and in analogy to the elastoviscoplastic case examined in Simo and Honein (cf. Simo, J.C., Honein, T., 1990. J. Appl. Mech. 57, 488-497). Her e the existence of the equilibrium response functional with respect to whic h the overstress is measured, and the existence of an instantaneous elastic response (Haupt, P., 1993. Acta Mech. 100, 129-154; Krempl, E., 1996. Unif ied Constitutive Laws of Plastic deformation. Academic Press, San Diego; Ts akmakis, Ch., 1996a. Acta Mech. 115, 179-202) are assumed. A broad set of o verstress functions turns out to characterize the class of models derived h erein. Both the flow rule for the viscoplastic deformation and the rate for m of the constitutive equation for the class of models cited above are obta ined, and the behavior of this equation under very slow strain rates and ve ry high viscosity is investigated. A numerical simulation is also given by selecting two overstress functions available in the literature (Haupt, P., Lion, A., 1993. Continuum Mech. Thermodyn. 7, 73-90; Krempl, E., Yao, D., 1 987. In: Rie, K.T. (Ed.), Low-Cycle Fatigue and Elasto-Plastic Behavior of Materials. Elsevier, New York, pp. 137-148). Loading conditions of repeated strain rate variation, monotonic strain rate with relaxation and cyclic lo ading at different strain rates are examined, and qualitative agreement is shown with the experimental observations done in Krempl and Kallianpur and Haupt and Lion (cf. Krempl, E., Kallianpur, V.V., 1984. J. Mech. Phys. Soli ds 32(4), 301-304; Haupt, P., Lion, A., 1993. Continuum Mech. Thermodyn. 7, 73-90) and references cited therein). (C) 2000 Elsevier Science Ltd. All r ights reserved.