Some symmetry group aspects of perfect plane plasticity system

TL;DR

This paper explores the symmetry properties of classical solutions in plane perfect plasticity, constructing slip-line equations, boundaries, and invariant velocity solutions, enhancing understanding of plastic flow behavior.

Contribution

It introduces a symmetry-based approach to derive slip-line solutions, boundaries, and velocity fields in plane perfect plasticity, linking group theory with plasticity solutions.

Findings

Explicit slip-line boundary equations derived

Invariant velocity solutions constructed for Prandtl stresses

Symmetry methods clarify plastic flow structures

Abstract

In this paper, all the known classical solutions of plane perfect plasticity system under 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 permits to determine explicitly boundaries of plastic areas. It is shown, how one can determine the compatible velocity solution for known stresses, considering symmetries. Some invariant solutions of velocities for Prandtl stresses are constructed. The mechanical sense of obtained velocity fields is discussed.