 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| Yu. N. Radaev, "On the hyperbolicity of 3D plasticity equations in isostatic coordinates," Mech. Solids. 43 (5), 756-764 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
5 |
Pages |
756-764 |
| DOI |
10.3103/S0025654408050105 |
| Title |
On the hyperbolicity of 3D plasticity equations in isostatic coordinates |
| Author(s) |
Yu. N. Radaev (Samara State University, Akad. Pavlova 1, Samara, 443011, Russia, radayev@ssu.samara.ru) |
| Abstract |
We consider the problem of classifying partial differential equations of the three-dimensional problem of ideal plasticity (for stress states corresponding to an edge of the Tresca prism) and the problem of finding a change of independent variables reducing these equations to the simplest normal Cauchy form. The original system of equations is represented in an isostatic coordinate system and is substantially nonlinear. We state a criterion for the simplest normal Cauchy form and find a coordinate system reducing the original system to the simplest normal Cauchy form. We show that the condition obtained in the present paper for a system to take the simplest normal form is stronger than the Petrovskii t-hyperbolicity condition if t is understood as the canonical isostatic coordinate whose level surfaces in space form fibers normal to the principal direction field corresponding to the maximum (minimum) principal stress. |
| Received |
02 December 2005 |
| Link to Fulltext |
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