Qualitative behaviour of viscoplastic solutions in the vicinity of maximum-friction surfaces

Abstract

The maximum-friction surface is a source of singular solution behaviour for several rate-independent plasticity models. Solutions based on conventional viscoplastic models do not show such behaviour. For a class of materials, there is a range of temperatures and/or strain rates where a necessity of the consideration of rate effects depends on the area of application of the final result. Hence, the same material under the same conditions can be represented by either rate-independent or rate-dependent models. In this case, a reasonable requirement is that viscous effects should not be very significant and, in particular, the qualitative behaviour of viscoplastic solutions should be similar to that of solutions based on rate-independent models. The present paper deals with this issue by means of the solution for simultaneous shearing and expansion of a hollow cylinder under plane-strain deformation. One of the goals of the paper is to show that there is a class of viscoplastic models satisfying the requirement formulated. The other goal is to find an asymptotic representation of the solution in the vicinity of the maximum-friction surface and compare it with the rigid perfectly plastic solution.