 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| 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 |
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(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
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[in Russian]. |
| 4. | R. Hill,
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[in Russian]. |
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| 8. | Yu. N. Radaev,
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(Izdat. Samara Univ., Samara, 2006)
[in Russian]. |
| 9. | A. Haar and T. Karman,
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in Plasticity Theory,
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(Izdat. Inostr. Liter., Moscow, 1948),
pp. 41-56
[in Russian]. |
| 10. | M. Levy,
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beyond Elastic Limits,"
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(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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