Viscoplasticity for instabilities due to strain softening and strain-rate softening

摘要

Three viscoplastic approaches are examined in this paper. First, the overstress viscoplastic models (i.e. the Perzyna model and the Duvaut-Lions model) are outlined. Next, a consistency viscoplastic approach is presented. In the consistency model a rate-dependent yield surface is employed while the standard Kuhn-Tucker conditions for loading and unloading remain valid. For this reason, the yield surface can expand and shrink not only by softening or hardening effects, but also by softening/hardening rate effects. A full algorithmic treatment is presented for each of the three models including the derivation of a consistent tangential stiffness matrix. Based on a limited numerical experience it seems that the consistency model shows a faster global convergence than the overstress approaches. For softening problems all three approaches have a regularising effect in the sense that the initial-value problem remains well-posed. The width of the shear band is determined by the material parameters and, if present, by the size of an imperfection. A relation between the length scales of the three models is given. Furthermore, it is shown that the consistency model can properly simulate the so-called S-type instabilities, which are associated with the occurrence of travelling Portevin-Le Chatelier bands.