Solution asymptotics near maximum friction surfaces in plane strain block compression: various viscoplastic laws with a saturation stress

The maximum friction requires that the friction stress is equal to the local shear yield stress of material. This law can be a source of singularities in rigid plastic solutions, including rigid viscoplastic solutions. For this reason, many classical solutions of rigid plasticity (rigid perfectly plastic solids) cannot be generalised when conventional rigid viscoplastic models are adopted. In the present paper, as class of rigid viscoplastic models with a saturation stress permitting for a generalisation of the famous Prandtl's solution for compression of a block between two parallel rough plates are considered and the corresponding generalisation of the solution is obtained.