 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| I. A. Solomeshch and M. A. Solomeshch, "Elastoplastic equations with exact consistency of strains for the elastic strain frame and the velocities of points," Mech. Solids. 40 (6), 13-29 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
6 |
Pages |
13-29 |
| Title |
Elastoplastic equations with exact consistency of strains for the elastic strain frame and the velocities of points |
| Author(s) |
I. A. Solomeshch (Israel)
M. A. Solomeshch (Israel) |
| Abstract |
We obtain an exact strain consistency equation for full, elastic, and
plastic strain characteristics that have a clear physical meaning and are
naturally related to stresses. The dynamic equations are represented in a
form that does not use the objective stress rate. This obviates a number of
essential difficulties in the theory of finite elastoplastic strains. |
| References |
| 1. | I. A. Solomeshch and M. A. Solomeshch, "The elastoplasticity
equations for the elastic strain frame and the velocities of points,"
Doklady RAN, Vol. 354, No. 6, pp. 759-761, 1997. |
| 2. | P. M. Naghdi, "A Critical review of the state of finite
plasticity," ZAMP, Vol. 41, No. 3, pp. 315-394, 1990. |
| 3. | A. S. Khan and S. Huang, Continuum Theory of Plastisity, Wiley, New
York, 1995. |
| 4. | A. Reuss, "Berücksichtigung der elastischen Formänderung in
der Plastizitätstheorie," ZAMM, Vol. 10, No. 3, pp. 266-274, 1930. |
| 5. | A. E. Green and P. M. Naghdi, "A general theory of an
elastic-plastic continuum," Arch. Ration. Mech. Anal., Vol. 18, No. 4,
pp. 251-281, 1965. |
| 6. | M. B. Rubin, "Plasticity theory formulated in terms of physically
based microstructural variables," Intern. J. Solids Structures. 1994. V.
31.19. P. 2615-2634. |
| 7. | J. F. Besseling and E. van der Giessen, Mathematical Modelling of
Inelastic Deformation, Chapman and Hall, London, 1994. |
| 8. | C. Eckart, "The thermodynamics of irreversible processes. IV. The
theory of elasticity and plasticity," Phys. Rev., Vol. 73, No. 4,
pp. 373-382, 1948. |
| 9. | P. M. Naghdi and A. R. Srinivasa, "A dynamical theory of structured
solids. I. Basic developments," Phil. Trans. Roy. Soc. London. Ser. A,
Vol. 345, No. 1677, pp. 425-458, 1993. |
| 10. | E. H. Lee and D. T. Liu, "Finite-strain elastic-plastic theory
with application to plane-wave analysis," J. Appl. Phys., Vol. 38, No. 1,
pp. 19-27, 1967. |
| 11. | A. V. Shitikov, "On a variational principle for the construction
of the elastoplasticity equations at finite strains," PMM [Applied
Mathematics and Mechanics], Vol. 59, No. 1, pp. 158-161, 1995. |
| 12. | P. Ciarlet, Mathematical Elasticity [Russian translation], Mir,
Moscow, 1992. |
| 13. | A. A. Il'yushin, Continuum Mechanics, Izd-vo MGU, Moscow, 1990. |
| 14. | R. Hill, The Mathematical Theory of Plasticity [Russian
translation], Gostekhizdat, Moscow, 1956. |
|
| Received |
26 June 2002 |
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