Some symmetry group aspects of perfect plane plasticity system
Mathematical Physics
2017-03-01 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1304.8115,
title = {Some symmetry group aspects of perfect plane plasticity system},
author = {Sergey I. Senashov and Alexander Yakhno},
journal= {arXiv preprint arXiv:1304.8115},
year = {2017}
}
Comments
19 pages, 9 figures