Velocity field equations and strain localization in rigid-plastic materials

Abstract The velocity field equations are set up for a standard rigid-plastic material. They allow a direct determination of the velocity field, and therefore correspond to the Navier-Stokes equations of a Newtonian fluid. Under conditions of plane strain or axisymmetric deformation, the velocity field equations lead, using the Levy-Huber-von Mises flow law, to the principal lines—i.e. to the trajectories of the principal strain-rates as characteristics. However, an incipient strain localization, combined with a velocity discontinuity, cannot be expected to occur along a principal line. Rather, a degeneration of the velocity field equations, shown to exist for certain rate-sensitive materials. might be responsible for such a localization effect.