 | | 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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| V. N. Kukudzhanov, "Decomposition method for elastoplastic equations," Mech. Solids. 39 (1), 73-80 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
1 |
Pages |
73-80 |
| Title |
Decomposition method for elastoplastic equations |
| Author(s) |
V. N. Kukudzhanov (Moscow) |
| Abstract |
A new method for the integration of equations governing the
behavior of elastoplastic media is proposed. This method is based
on the decomposition of the constitutive relations for relaxation
media with respect to physical processes. We show that for the
classical elastoplastic medium independent of the time scale, the
decomposition leads to an algebraic power-law equation for the
correction coefficient of the elastic solution. In the case of
perfect plasticity, this coefficient coincides with that obtained
in [1]. For more general models, this coefficient can also be
expressed in closed form.
For elastoviscoplastic media, the decomposition leads to a
differential equation for the correction coefficients that in this
case are functions of time. The solution of this differential
equation is obtained in an analytical form. This allows one to
investigate the convergence of the numerical method and to
determine asymptotic properties of this method.
The proposed method has computational advantages as compared with
the standard iteration methods. At each integration step, this
method involves the solution of an elasticity problem and the
solution of one equation for the correction coefficients at the
corrector stage. In contrast to this, the traditional methods
require solving a system of n constitutive equations (ngeq6)
at each point of the body. |
| References |
| 1. | M. L. Wilkins, "Numerical analysis of elastoplastic flows,"
in B. Alder, S. Fernbach, and M. Rotenberg
(Editors), Fundamental Methods in Hydrodynamics [Russian translation],
pp. 212-263, Mir, Moscow, 1967. |
| 2. | E. Hinton and D. R. J. Owen, Finite Elements in
Plasticity, Pineridge Press, Swaensea, 1981. |
| 3. | V. M. Fomin, A. I. Gulidov, G. A. Sapozhnikov, et al.,
High-speed Interaction of Bodies [in Russian], Izd-vo SO RAN,
Novosibirsk, 1999. |
| 4. | V. V. Sokolovskii, Theory of Plasticity [in Russian],
Vysshaya Shkola, Moscow, 1969. |
| 5. | N. G. Burago and V. N. Kukudzhanov, Solution of
Elastoplastic Problems by the Finite Element Method. A Software
Package "Astra." Preprint No. 326 [in Russian], Institute for
Problems in Mechanics of the USSR Academy of Sciences, Moscow, 1988. |
| 6. | V. M. Sadovskii, Discontinuous Solutions in Dynamics of
Elastoplastic Media [in Russian], Nauka, Moscow, 1997. |
| 7. | G. Duvant and J.-L. Lions, Inequalities in Mechanics and
Physics [Russian translation], Nauka, Moscow, 1980. |
| 8. | V. N. Kukudzanov, Difference Methods for Solving Problems
in Mechanics of Solids [in Russian], MFTI, Moscow, 1992. |
| 9. | G. I. Marchuk, Decomposition Methods [in Russian], Nauka, Moscow, 1988. |
| 10. | V. M. Kovenya and N. N. Yanenko, The Decomposition Method
in Gas Dynamics [in Russian], Nauka, SO AN SSSR, Novosibirsk. |
| 11. | O. M. Belotserkovskii and Yu. M. Davidov, The Method of Large Particles
in Gas Dynamics [in Russian], Nauka, Moscow, 1982. |
| 12. | V. N. Kukudzhanov and Yu. I. Kudryashev, Solution of Mixed
Problems of Unsteady Interaction of Gaseous Media with Solids.
Preprint No. 472 [in Russian], Institute for Problems in Mechanics of the
USSR Academy of Sciences, Moscow, 1990. |
| 13. | V. Yu. Kibardin and V. N. Kukudzhanov, "Modeling of continuum fracture in an elastoviscoplastic material," Izv. AN. MTT [Mechanics of Solids],
No. 1, pp. 109-123, 2001. |
| 14. | V. N. Kukudzhanov, "Numerical simulation of dynamical processes
of deformation and fracture in elastoplastic media," Uspekhi Mekhaniki
[Advances in Mechanics], Vol. 8, No. 4, pp. 21-65, 1985. |
| 15. | O. Zienkiewicz, The Finite Element Method in Engineering
Sciences [Russian translation], Mir, Moscow, 1875. |
| 16. | C. A. Brebbia, J. C. F. Telles, and L. C. Wrobel, Boundary
Element Techniques [Russian translation], Mir, Moscow, 1987. |
| 17. | V. N. Kukudzhanov, "Wave propagation in elastic-viscoplastic materials
with a general stress-strain diagram," Izv. AN. MTT [Mechanics of Solids],
No. 5, pp. 96-111, 2001. |
|
| Received |
16 October 2003 |
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