 | | 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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| E. A. Davydova and A. N. Sakharov, "A flow of an isotropically hardening rigid-plastic material in plane channels," Mech. Solids. 36 (6), 107-112 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
6 |
Pages |
107-112 |
| Title |
A flow of an isotropically hardening rigid-plastic material in plane channels |
| Author(s) |
E. A. Davydova (Moscow)
A. N. Sakharov (Moscow) |
| Abstract |
In the framework of the theory of isotropically hardening rigid-plastic
material [1], a problem of steady-state plane flow is considered. In
contrast to the problems of flow of perfectly plastic solids where
the equilibrium equations have integrals (Henky integrals), the equilibrium
equations for hardening materials are nonintegrable [2]. This fact
complicates the utilization of direct numerical methods (e.g. a grid
method), since in the process of solution it is necessary to find the flow
lines of particles in order to determine the hardening parameter. Note that
the hardening parameter ϰ is determined for a particle of the
material. Therefore, to find the value of this parameter in the Eulerian
coordinate system it is necessary to trace the entire history of its
variation along the path of the particle to the given point (x, y) of
space. Hence, we should use the Lagrangian approach when determining the
hardening parameter of the material particles. However, as shown in [2],
this difficulty can be overcome in the case of steady-state flow. The aim
of the present paper is to investigate the flow in a plane channel and
analyze the solution of the problem for plane deformation on the basis of
the theory of isotropic hardening. |
| References |
| 1. | D. D. Ivlev and G. I. Bykovtsev, Theory of a Hardening Plastic
Solid [in Russian], Nauka, Moscow, 1971. |
| 2. | V. D. Klyushnikov, "A plane steady-state flow of a hardening
rigid-plastic material," Doklady AN SSSR, Vol. 303, No. 4, pp. 815-817,
1988. |
| 3. | D. A. Kikvidze, L. A. Koryakin, and A. N. Sakharov, "A
semi-inverse method for solving problems of a steady-state flow of a
rigid-plastic material with hardening," Izv. AN. MTT
[Mechanics of Solids], No. 6, pp. 79-85, 1993. |
| 4. | V. V. Novozhilov, Fundamentals of the Nonlinear Theory of
Elasticity [in Russian], Gostekhizdat, Moscow, Leningrad, 1948. |
| 5. | V. V. Sokolovskii, Theory of Plasticity [in Russian], Vysshaya
Shkola, Moscow, 1969. |
| 6. | D. V. Georgievskii, Stability of Deformation Processes in
Viscoplastic Solids [in Russian], URSS, Moscow, 1998. |
|
| Received |
25 February 1999 |
| << Previous article | Volume 36, Issue 6 / 2001 | Next article >> |
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