 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13653 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8223
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| In English (Mech. Solids): | | 5430 |
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| Yu.N. Radaev, "Boundary Conditions for Three-Dimensional States of Plastic Solids," Mech. Solids. 60 (8), 6691-6704 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
8 |
Pages |
6691-6704 |
| DOI |
10.1134/S0025654425607554 |
| Title |
Boundary Conditions for Three-Dimensional States of Plastic Solids |
| Author(s) |
Yu.N. Radaev (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, radayev@ipmnet.ru, y.radayev@gmail.com) |
| Abstract |
In this paper, the formulation of boundary-value problems in perfect plasticity is considered
for the stress states corresponding to an edge of the Coulomb-Tresca prism. Solving three-dimensional
problems in perfect plasticity requires the formulation of boundary conditions on the surface of a perfectly plastic solid. There are no difficulties in determining the boundary data for the stress tensor in
the plane and axisymmetric cases. In three-dimensional case, setting the boundary conditions is associated with solving the problem of determining the orientations of the principal directions of the stress
tensor, corresponding to the greatest (or lowest) principal normal stress, on the surface of the solid.
It has been shown that, on the free boundary surface, the vector field, indicating the principal directions corresponding to the greatest (or lowest) principal normal stress, is surface-irrotational, and
therefore its trajectories are geodesic. |
| Keywords |
plasticity, Coulomb-Tresca prism, principal normal stresses, Gaussian curvature, geodesic |
| Received |
02 September 2025 | Revised |
18 December 2025 | Accepted |
20 December 2025 |
| Link to Fulltext |
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