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 discretization of the continuum theory based on the mentioned principles considered as separate equations. 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.

在这项工作中，一致的粘塑性公式是从热力学原理得出的，并采用了连续弹性校正率的概念。该模型是基于最大粘塑性耗散原理来确定流动方向而开发的。该模型使用等效粘塑性应变及其速率作为状态变量。功率平衡和能量平衡分别给出了等效的粘塑性应变率和粘塑性应变的独立演化方程，前者用无粘性速率表示。几个关键点将我们的提法与其他建议区分开来。首先，粘塑性应变速率（而不是屈服函数）始终将反向加载过程中的保守行为与耗散行为区分开来。离散隐式积分算法是基于提到的被视为独立方程的原理的连续论的直接离散化。第二，通过简单地将粘度设置为零，以良好状态回收粘性溶液。实际上，无粘性，粘弹性和粘塑性是我们的配方和积分算法的特例，只需将相应的参数设置为零（粘度或屈服应力）即可恢复无粘性。第三，对于比例加载情况，可以采用精确的方式获得线性粘塑性解，而与所采用的时间步长无关。四个一般的非线性模型（Perzyna，Norton等）可以作为特殊情况立即纳入理论和计算实现中。