A comparison of viscoplasticity formats and algorithms

Algorithmic issues for the two thermodynamically consistent viscoplastic formulations of Perzyna and Duvaut–Lions are discussed. It is shown that it is simple to avoid the numerical problems associated with a small relaxation time without resorting to elaborate perturbation techniques, as suggested in the literature. A systematic numerical investigation of the efficiency of Newton iterations, that employ the Algorithmic Tangential Stiffness (ATS) tensor, as compared to various approximations, is carried out for a cohesive-frictional model with non-linear isotropic hardening. Generally, the ATS-tensor is formulated in such an explicit fashion that its tensorial structure resembles that of the underlying rate-independent continuum stiffness. For both the Perzyna and the Duvaut–Lions format, it appears that the ATS-tensor is obtained by a proper augmentation of the corresponding rate-independent ATS-tensor. Copyright © 1999 John Wiley & Sons, Ltd.