Motion of a rigid bar in a rigid-viscoplastic medium: The influence of the model type on the solution behavior

Abstract

The paper deals with rigid-plastic materials satisfying the vonMises plasticity condition under the assumption that their yield point in pure shear depends only on the equivalent strain rate (rigid-viscoplastic material models). The rigid-viscoplastic models are classified by the yield point behavior in pure shear as the equivalent strain rate tends to zero or infinity. All in all, four classes of rigid-viscoplastic material models are distinguished. For each of these classes of material models, the solution is constructed for the translational motion of an axisymmetric rigid bar along its symmetry axis in a rigid-plastic medium. It is assumed that the maximum friction law acts on the surface of contact between the bar and the rigid-viscoplastic medium. It is shown that the solutions provided by models of different classes qualitatively differ from each other. A qualitative comparison with experimental results known in the literature is carried out. It is shown that predicting the formation of an intensive plastic deformation layer near the friction surface, which is observed in experiments, is possible if the rigid-viscoplastic model contains the saturation stress (the stress, bounded in magnitude, to which the yield point in pure shear tends as the equivalent strain rate tends to infinity).