Quasi-static axially symmetric viscoplastic flows near very rough walls

Abstract

a b s t r a c tThe paper deals with asymptotic behavior of viscous and viscoplastic solutions in the vicinity of very rough walls under conditions of axial symmetry. The constitutive equations adopted include a saturation stress. A distinguished feature of this model is that the regime of sticking at the wall may be incompatible with other boundary conditions. In this case the regime of sliding must occur and solutions are singular in the vicinity of such surfaces. The exact asymptotic representation of the singular solutions is controlled by the dependence of the equivalent stress on the equivalent strain rate as the latter approaches infinity. There exist such dependences that the viscoplastic model possesses a smooth transition of qualitative behavior between rigid perfectly plastic and viscoplastic solutions, and this may prove to be advantageous for some applications.

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers

“…In particular, the quadratic invariant of the strain-rate tensor can approach infinity near the friction surface. This feature of solution behavior has been demonstrated in [8] for rigid perfectly-plastic material and in [9,10] for viscoplastic material with a saturation stress. Additionally, numerous analytic and semi-analytic solutions for various material models reveal this behavior of solutions [1,2,11,12,13,14,15].…”

“…The possibility to extend this result to rate-dependent models should depend on the way the viscosity is introduced into the model. By analogy to rate-dependent models of pressure-independent plasticity [9,10], it is reasonable to expect that singular asymptotic solutions may appear in the case of vanishing viscosity.…”