VISCOPLASTIC MODELLING OF STATIC AND DYNAMIC INSTABILITIES

摘要

A classification of plastic instabilities in terms of phenomenologieal material parameters is given by using a linear stability analysis. Secondly, the viscoplastic modelling of localisation problems is discussed with overstress viscoplastic models (i.e. the Perzyna model and the Duvaut-Lions model) and with a consistency viscoplastic model. In the overstress viscoplastic models, the evolution of the viscoplastic How is constrained by the plastic relaxation equations and is directly defined in the stress space. In the consistency model a rate-dependent yield surface is employed and the viscoplastic flow is determined by the standard Kuhn-Tucker conditions. For softening problems all three models 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. Finally, stationary instabilities (shear bands) and propagative instabilities (Portevin Le-Chatelier bands) are simulated by means of finite elements.