The transition of qualitative behaviour between rigid perfectly plastic and viscoplastic solutions

Abstract

An incompressible rigid viscoplastic material is confined between two planar plates which are inclined at an angle $$2\alpha $$ . In a certain sense, the viscoplastic model adopted approaches rigid perfectly plastic models as the equivalent strain rate approaches zero and infinity. The plates intersect in a hinged line, and the angle $$\alpha $$ slowly decreases from an initial value. The maximum-friction law is assumed at the plates. A boundary value problem for the flow of the material is formulated, and its asymptotic analysis is carried out near the friction surface. The solution may exhibit sliding or sticking at the plates. Solutions which exhibit sticking may have a rigidly rotating zone in the region adjacent to the plates. Solutions which exhibit sliding are singular. Solutions which exhibit sticking may also be singular under certain conditions. In general, there are several critical values of $$\alpha $$ at which changes in the qualitative behaviour of the solution occur. Qualitative features of the solution found are compared with those of the solution for the classical rigid plastic model.