 | | 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: | | 13362 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8178
|
| In English (Mech. Solids): | | 5184 |
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| Y.N. Radaev, "On Additional Tensor Symmetry Relation in the Mathematical Theory of Perfect Plasticity," Mech. Solids. 60 (5), 3528-3540 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
5 |
Pages |
3528-3540 |
| DOI |
10.1134/S0025654425603921 |
| Title |
On Additional Tensor Symmetry Relation in the Mathematical Theory of Perfect Plasticity |
| Author(s) |
Y.N. Radaev (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, radayev@ipmnet.ru, y.radayev@gmail.com) |
| Abstract |
The paper presents fundamental principles of the mathematical theory of plasticity for spatial states, corresponding to an edge of the Coulomb–Tresca prism, when the flow of a body is governed by generalized associated flow rule. A detailed analysis is provided for the relations resulting from the generalized flow rule for an isotropic body, associated with the Tresca yield condition, and restricting the freedom of plastic flow to the minimum extent for the specified states. It has been shown that the spatial relations of plasticity theory formulated by A.Yu. Ishlinskii in 1946 follow from the generalized version of the flow theory. It has been established that the constitutive relations of Ishlinskii for the states on the edge of the Coulomb–Tresca prism express the commutativity of the stress and plastic strain increment tensors. An additional tensor symmetry relation is obtained by applying this commutativity relation. |
| Keywords |
perfect plasticity, Coulomb–Tresca prism, associated flow rule, commutativity |
| Received |
30 June 2025 | Revised |
06 July 2025 | Accepted |
07 August 2025 |
| Link to Fulltext |
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