Compression of a viscoelastic layer between rough parallel plates

If the maximal friction law is applied, then some generalizations of the Prandtl solution for the compression of a plastic layer between rough plates do not exist. In particular, this pertains to the viscoplastic solutions obtained earlier. In the present paper, we show that these solutions do not exist because of the properties of the model material and introduce a model for which this solution can be constructed. The obtained solution is singular. In particular, the equivalent strain rate tends to infinity as the friction surface is approached, and its asymptotic behavior exactly coincides with that arising in the classical solution. The obtained solution is illustrated by numerical examples, which, in particular, show that an extremely thin boundary layer may arise near the friction surfaces.