Planar plastic flow of polymers near very rough walls

The main objective of the present paper is to investigate, by means of a boundary value problem permitting a semi-analytic solution, qualitative behaviour of solutions for two pressure-dependent yield criteria used for plastically incompressible polymers. The study mainly focuses on the regime of friction (sticking and sliding). It is shown that the existence of the solution satisfying the regime of sticking depends on other boundary conditions. In particular, there is such a class of boundary conditions depending on the yield criterion adopted that the regime of sliding is required for the existence of the solution independently of the friction law.