Speed discontinuities
Plasticity in forming

RPP behavior is mathematically compatible with the existence of velocity discontinuities along internal metal surfaces S_c. Physically, these velocity discontinuities represent zones where the velocity field exhibits very high gradients, as can be seen, for example, at the boundary of the "dead" (quasi-rigid) zones that form in the vicinity of tools in the forging of solid products ("blacksmith's cross"), in the rolling of heavy plates, in flat-die spinning [21], and in the primary shear giving rise to the machining chip [44].

Due to the conservation of mass and incompressibility, the discontinuity can only be tangent to S_c and the velocity...