On the consistency of viscoplastic formulations

A viscoplastic consistency condition is incorporated into the traditional viscoplastic rate format with two objectives in mind: (i) to develop a tangential material operator for rate sensitive behavior similarly to rate independent elastoplasticity, and (ii) to make an analytical reference solution available for evaluating the accuracy of new and well-established computational strategies to integrate the viscoplastic evolution equations. The viscoplastic tangent operator provides the missing link between rate independent plasticity and rate dependent viscoplasticity. It also furnishes the acoustic tensor, which is required for localization analysis of discontinuous failure. Besides the formulation of the viscoplastic tangent operator, we present an analytical reference solution for perfect J2 viscoplasticity. This analytical result is subsequently used to determine the accuracy of simplifying assumptions behind the algebraic evaluation of the viscoplastic multiplier, and to quantify the error of the radial return mapping strategy for viscoplastic computations