On a mechanical analogy in the ideal plasticity theory

The Cauchy problem of propagation of plastic state zones in a boundless medium from the boundary of a convex surface, along which normal pressure and shear forces act, is considered. In the case of complete plasticity, the Tresca system of quasi-static equations of ideal plasticity, which describes the stress-strain state of the medium, is known to be hyperbolic and to be similar to a system that describes a steady-state flow of an ideal incompressible fluid. This system is numerically solved with the use of a difference scheme applied for hyperbolic systems of conservation laws. Results of numerical calculations are presented.