 | | 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
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 44, Issue 2 / 2009 | Next article >> |
| N. D. Verveyko and A. V. Kuptsov, "Method of characteristics for the 3D perfect plasticity problem with the von Mises yield criterion," Mech. Solids. 44 (2), 322-332 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
2 |
Pages |
322-332 |
| DOI |
10.3103/S0025654409020186 |
| Title |
Method of characteristics for the 3D perfect plasticity problem with the von Mises yield criterion |
| Author(s) |
N. D. Verveyko (Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia, ver38@mail.ru)
A. V. Kuptsov (Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia, smartandrew@mail.ru) |
| Abstract |
We present a linearized system of partial differential equations for the three-dimensional perfect plasticity problem with the von Mises yield criterion. We construct the characteristics of the three-dimensional problem, obtain differential relations along the characteristic planes, and devise a consistent stable finite-difference scheme. The use of conditions on the stress discontinuity surfaces permits simultaneously solving the Cauchy, Goursat, and mixed problems. |
| References |
| 1. | D. D. Ivlev, Theory of Ideal Plasticity (Nauka, Moscow, 1966) [in Russian]. |
| 2. | D. D. Ivlev, Mechanics of Plastic Media, Vol. 1 (Fizmatlit, Moscow, 2001) [in Russian]. |
| 3. | N. D. Verveiko and A. V. Kuptsov, "To Static Definability of the Spatial Problem of Theory of Ideal Plasticity," Vestnik EGU, No. 1, 143–152 (2006). |
| 4. | N. D. Verveyko and A. V. Kuptsov, "Admissible Versions of Total Plasticity of Spatial Problems of Ideal Plasticity under the Mises Condition," Vestnik PMM, No. 6, 28–31 (2007) [Izd-vo VGU, Voronezh, 2007]. |
| 5. | N. D. Verveyko and A. V. Kuptsov, "The Method of Iterations for Solution of Tasks of the Plastic Theory," Vestnik VGU. Ser. Fiz. Mat., No. 1, 149–153 (2005). |
| 6. | V. V. Sokolovskii, The Theory of Plasticity (Vysshaya Shkola, Moscow, 1969) [in Russian]. |
| 7. | V. N. Kukudzhanov, "Numerical Modeling of Dynamical Processes of Deformation and Fracture of Elastoplastic Media," Uspekhi Mekh. 8(4), 21–65 (1985). |
| 8. | Yu. N. Radaev and L. A. Kurnysheva, "Three-Dimensional Equations of a Mixed Problem of Mathematical Theory of Plasticity," Vestnik ChGPU im. Yakovleva. Mekh. Predelnogo Ravnovesiya, No. 1, 90–120 (2007). |
| 9. | L. I. Sedov, Mechanics of Continuous Media, Vol. 1 (Fizmatlit, Moscow, 1970) [in Russian]. |
| 10. | L. M. Kachanov, Foundations of the Theory of Plasticity (Gostekhizdat, Moscow, 1956; North-Holland, Amsterdam, 1971). |
|
| Received |
10 April 2006 |
| Link to Fulltext |
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