Abstract
In this paper, all the known classical solutions of a plane perfect plasticity system under the Saint Venant–Tresca–von Mises yield criterion are associated with some group of point symmetries. The equations of slip-line families for all solutions are constructed, which allows one to explicitly determine the boundaries of the plastic areas. It is shown how one can determine the compatible velocity solution for known stresses by considering symmetries. Some invariant solutions of velocities for Prandtl stresses are constructed. The mechanical sense of the obtained velocity fields is discussed.To the blessed memory of our teacher D D Ivlev
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More From: Journal of Physics A: Mathematical and Theoretical
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