Singular solutions in an axisymmetric flow of a medium obeying the double shear model

An asymptotic analysis of equations of an axisymmetric flow of a rigid-plastic material obeying the double shear model in the vicinity of surfaces with the maximum friction is performed. It is shown that the solution is singular if the friction surface coincides with the envelope of the family of characteristics. A possible character of the behavior of singular solutions in the vicinity of surfaces with the maximum friction is determined. In particular, the equivalent strain rate in the vicinity of the friction surface tends to infinity in an inverse proportion to the square root from the distance to this surface. Such a behavior of the equivalent strain rate is also observed in the classical theory of plasticity of materials whose yield condition is independent of the mean stress.