General nonlinear constitutive equations for a thermoelastic-viscoplastic material that exhibits a rate-dependent yield strength are developed by assuming that the yield function depends explicitly on the total strain rate and temperature rate. Following recent developments in continuum thermodynamics restrictions on the constitutive response functions are imposed to ensure that the moment of momentum and energy equations are identically satisfied and that various statements of the second law of thermodynamics are satisfied for all thermodynamical processes. A particular constitutive equation for a thermoelastic-viscoplastic material is proposed, and an analytical example is considered that examines the rate-dependent plastic response to a deformation history that includes segments of loading, unloading, and reloading, each occurring at varying strain rates.

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