| | 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: | | 12788 |
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8028
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In English (Mech. Solids): | | 4760 |
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<< Previous article | Volume 47, Issue 6 / 2012 | Next article >> |
Yu.N. Radaev, "On Attainable Lower Boundary of the Three-Dimensional Coulomb-Tresca Invariant," Mech. Solids. 47 (6), 671-676 (2012) |
Year |
2012 |
Volume |
47 |
Number |
6 |
Pages |
671-676 |
DOI |
10.3103/S002565441206009X |
Title |
On Attainable Lower Boundary of the Three-Dimensional Coulomb-Tresca Invariant |
Author(s) |
Yu.N. Radaev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, radayev@ipmnet.ru, y.radayev@gmail.com) |
Abstract |
An attainable lower boundary of the three-dimensional Coulomb-Tresca invariant is constructed to facilitate the search of plasticity conditions for isotropic bodies which, just as the Tresca-Saint Venant plasticity condition, ensure the hyperbolic analytic type of three-dimensional equations of the mathematical theories of plasticity based on the generalized associate flow law. The construction is performed by using the system of three "two-dimensional" tangential stresses related to the given three-dimensional stress state. It is proved that the Coulomb-Tresca invariant attains its lower bound in any plane strain state where the out-of-plane principal normal stress is intermediate (or median). |
Keywords |
ideal plasticity, yield, yield point, Coulomb-Tresca prism, tangential stress, principal stress |
References |
1. | C. A. Coulomb,
"Essay sur l'Application des Régles de Maximes et Minimis á Quelques Problemes de Statique, Relatifs a l'Archutecture,"
in Mémoirs de Mathematique et de Physique,
Présentés a L'acádemie Royale des Sciences, Anno 1773, Vol. 7
(Paris de l'imprimerie Royale, Paris, 1776),
pp. 343-382. |
2. | A. Nadai,
Plasticity. Mechanics of Plastic State of Material
(McGraw-Hill, New York, 1931; ONTI, Moscow-Leningrad, 1936). |
3. | A. A. Il'yushin,
Plasticity
(Gostechizdat, Moscow, 1948)
[in Russian]. |
4. | R. Hill,
The Mathematical Theory of Plasticity
(Gostekhizdat, Moscow, 1956)
[in Russian]. |
5. | L. M. Kachanov,
Foundations of the Theory of Plasticity
(Nauka, Moscow, 1969; North-Holland, Amsterdam, 1971). |
6. | V. V. Sokolovskii,
The Theory of Plasticity
(Vysshaya Shkola, Moscow, 1969)
[in Russian]. |
7. | D. D. Ivlev,
Theory of Perfect Plasticity
(Nauka, Moscow, 1966)
[in Russian]. |
8. | Yu. N. Radaev,
Spatial Problem of Mathematical Theory of Plasticity
(Izdat. Samara Univ., Samara, 2006)
[in Russian]. |
9. | A. Haar and T. Karman,
"To the Theory of Stress States in Plastic and Granular Materials,"
in Plasticity Theory,
Ed. by Yu. N. Rabotnov
(Izdat. Inostr. Liter., Moscow, 1948),
pp. 41-56
[in Russian]. |
10. | M. Levy,
"To the Problem of General Equations of Internal Motions Arising in Rigid Plastic Bodies
beyond Elastic Limits,"
in Plasticity Theory,
Ed. by Yu. N. Rabotnov
(Izdat. Inostr. Liter., Moscow, 1948),
pp. 20-23
[in Russian]. |
11. | Yu. N. Radaev,
"To the Theory of Plane Strain of Ideally Plastic Bodies,"
Vestnik Samar. Gos. Univ. Estestvennonauchn. Ser.,
No. 3 (62), 272-289 (2008). |
12. | A. Yu. Ishlinskii,
"On Equations of Body Deformation beyond the Elasticity Limit,"
Uch. Zap. MGU. Mekh.,
No. 117, 90-108 (1946). |
13. | Yu. N. Radaev,
"On the Ishlinskii Commutation Relations in Mathematical Theory of Plasticity,"
Vestnik Samar. Gos. Univ. Estestvennonauchn. Ser.,
No. 6 (56), 102-114 (2007). |
14. | L. Mirsky,
"The Spread of a Matrix,"
Mathematika
3 (6), 127-130 (1956). |
|
Received |
03 August 2012 |
Link to Fulltext |
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