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In this work, a consistent viscoplasticity formulation is derived fromthermodynamical principles and employing the concept of continuum elasticcorrector rate. The proposed model is developed based on the principle ofmaximum viscoplastic dissipation for determining the flow direction. The modeluses both the equivalent viscoplastic strain and its rate as state variables.Power balance and energy balance give, respectively, separate evolutionequations for the equivalent viscoplastic strain rate and the viscoplasticstrain, the former written in terms of inviscid rates. Several key pointsdistinguish our formulation from other proposals. First, the viscoplasticstrain rate (instead of a yield function) consistently distinguishesconservative from dissipative behaviours during reverse loading; and thediscrete implicit integration algorithm is an immediate implementation of thecontinuum theory based on the mentioned principles. Second, the inviscidsolution is recovered in a well-conditioned manner by simply setting theviscosity to zero. Indeed, inviscid plasticity, viscoelasticity andviscoplasticity are particular cases of our formulation and integrationalgorithm, and are recovered just by setting the corresponding parameters tozero (viscosity or yield stress). Third, the linear viscoplasticity solution isobtained in an exact manner for proportional loading cases, independently ofthe time step employed. Four, general nonlinear models (Perzyna, Norton, etc)may be immediately incorporated as particular cases both in the theory and thecomputational implementation.

Thermodynamically consistent nonlinear viscoplastic formulation with  well-conditioned recovery of the inviscid solution: Theory and implicit  integration algorithm with exact solution for the linear case