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
