  In this work, a consistent viscoplasticity formulation is derived from
thermodynamical principles and employing the concept of continuum elastic
corrector rate. The proposed model is developed based on the principle of
maximum viscoplastic dissipation for determining the flow direction. The model
uses both the equivalent viscoplastic strain and its rate as state variables.
Power balance and energy balance give, respectively, separate evolution
equations for the equivalent viscoplastic strain rate and the viscoplastic
strain, the former written in terms of inviscid rates. Several key points
distinguish our formulation from other proposals. First, the viscoplastic
strain rate (instead of a yield function) consistently distinguishes
conservative from dissipative behaviours during reverse loading; and the
discrete implicit integration algorithm is an immediate implementation of the
continuum theory based on the mentioned principles. Second, the inviscid
solution is recovered in a well-conditioned manner by simply setting the
viscosity to zero. Indeed, inviscid plasticity, viscoelasticity and
viscoplasticity are particular cases of our formulation and integration
algorithm, and are recovered just by setting the corresponding parameters to
zero (viscosity or yield stress). Third, the linear viscoplasticity solution is
obtained in an exact manner for proportional loading cases, independently of
the time step employed. Four, general nonlinear models (Perzyna, Norton, etc)
may be immediately incorporated as particular cases both in the theory and the
computational implementation.
