On a mechanical analogy in the ideal plasticity theory

V. V. Alekhin, B. D. Annin, V. V. Ostapenko

Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia

Abstract: 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.

Keywords: Tresca ideal plasticity, complete plasticity, support function of a contour, equidistant surface, hyperbolic system of conservation laws.

UDC: 539.374

Received: 25.06.2007

 English version: Journal of Applied Mechanics and Technical Physics, 2008, 49:4, 580–586

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