Simple One-Dimensional Waves in an Incompressible Anisotropic Elastoplastic Medium with Hardening

We study simple one-dimensional waves (Riemann waves) in an incompressible anisotropic elastoplastic medium with hardening. The motion is parallel to the planes of constant phase. We show that there exist two types of such waves: fast and slow waves, whose velocities are different everywhere except for some points in the plane of stress components. The medium is assumed to be nonlinear and defined by its elastic properties as well as by conditions for the formation of plastic deformations. We find the velocities of the characteristics that carry the Riemann waves, and analyze the evolution of the Riemann waves and the overturning conditions for these waves.