Plane-strain compression of material obeying the double-shearing model between rotating plates

Nonsteady planar flow of a solid obeying the double-shearing model between two rough, inclined plates rotating about the same motionless line is considered. A semi-analytical solution to the problem is obtained. Attention is devoted to the singular behaviour of a velocity field in the vicinity of the friction surface. It is demonstrated that the velocity component tangent to the friction surface is describable by nondifferentiable functions and that the equivalent strain rate approaches infinity on the friction surface. Such a behaviour of the velocity field is compared with other solutions based on the double-shearing model and with a general result on the singular behaviour of velocity fields in classical plasticity of pressure-independent materials. The concept of strain rate intensity factor introduced in classical plasticity is extended to the double-shearing model of pressure-dependent plasticity. Some velocity distributions and strain intensity factor variations are calculated.