 | | 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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| S. A. Korneev, "Constitutive relations for viscoelastoplastic materials at small strains," Mech. Solids. 40 (3), 83-97 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
3 |
Pages |
83-97 |
| Title |
Constitutive relations for viscoelastoplastic materials at small strains |
| Author(s) |
S. A. Korneev (Omsk) |
| Abstract |
A thermomechanical approach to the modeling of viscoelastoplastic
materials at small strains is presented which allows the
experimentally observed effect of strain rate hardening of materials,
resulting in the dynamic yield stress exceeding the static yield
stress, to be described. An analysis of P. Perzyna's viscoplasticity
equations is carried out first, the equations being presented in an
alternative, though mathematically equivalent, form which agrees with
A. A. Il'yushin's macroscopic determinability principle.
The dynamic yield criteria (in stress and strain spaces) are derived,
together with the relationships for the irreversible strain variation laws
which are shown to coincide with the associated plastic flow rules. The
results obtained agree with the classical ones. For the corresponding
material parameters, the Tresca-Saint-Venant, Huber-Mises,
Ishlinskii-Prager, and Kadashevich-Novozhilov yield criteria are
obtained, as well as the Ivlev-Ishlinskii, Kaliszky, and Perzyna
dynamic yield surfaces. The constitutive relations considered cover,
as the limiting cases, the Kelvin, Maxwell, and Voigt viscoelastic body
models. The approach developed enables also the elastic (mechanical)
hysteresis to be taken into account. |
| References |
| 1. | W. Nowacki, Stress Waves in Non-elastic Solids [Russian translation],
Mir, Moscow, 1978. |
| 2. | P. Perzyna, Fundamentals of Viscoplasticity [Russian translation],
Mir, Moscow, 1968. |
| 3. | 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. |
| 4. | A. A. Il'yushin, Continuum Mechanics [in Russian], Izd-vo MGU,
Moscow, 1978. |
| 5. | Yu. I. Yagn and O. A. Shishmarev, "Some results of studying the boundaries of the elastic
state in plastically stretched nickel samples," Doklady AN SSSR, Vol. 119, No. 1,
pp. 46-48, 1958. |
| 6. | I. N. Izotov and Yu. I. Yagn, "Study of the plastic deformation of a metal with strain
anisotropy created by preloading," Doklady AN SSSR, Vol. 139, No. 3, pp. 576-579, 1961. |
| 7. | H. J. Ivey, "Plastic stress-strain relations and yield surfaces for
aluminum alloys," J. Mech. Eng. Sci., Vol. 3, No. 1, pp. 15-31, 1961. |
| 8. | I. N. Zverev, "Propagation of disturbances in a viscoelastic
and viscoplastic rod," PMM [Applied Mathematics and Mechanics], Vol. 14, pp. 295-302, 1950. |
| 9. | E. I. Shemyakin, "Propagation of nonlinear disturbances in a viscoelastic medium,"
Doklady AN SSSR, Vol. 104, No. 1, pp. 34-37, 1995. |
| 10. | P. M. Ogibalov and A. Kh. Mirzadzhanzade, Unsteady Motions of Viscoplastic Media [in Russian],
Izd-vo MGU, Moscow, 1970. |
| 11. | A. G. Kulikovskii and E. I. Sveshnikova, Nonlinear Waves in Elastic Media [in Russian], Mosk.
Litsei, Moscow, 1998. |
| 12. | L. I. Sedov, Continuum Mechanics [in Russian], Nauka,
Moscow, 1973. |
| 13. | B. D. Anin and V. M. Zhigalkin, Behavior of Materials Subjected to Complex Loading [in Russian],
Izd-vo SO RAN, Novosibirsk, 1999. |
| 14. | A. Yu. Ishlinskii and D. D. Ivlev, Mathematical Theory of Plasticity [in Russian], Fizmatlit,
Moscow, 2001. |
| 15. | A. Yu. Ishlinskii, Applied Problems in Mechanics. Book 1. Mechanics of Viscoplastic and
Imperfectly Elastic Bodies [in Russian], Nauka, Moscow, 1986. |
| 16. | L. M. Kachanov, Fundamentals of Plasticity Theory [in Russian], Nauka, Moscow, 1969. |
| 17. | N. N. Malinin, Applied Theory of Plasticity and Creep
[in Russian], Mashinostroenie, Moscow, 1975. |
| 18. | A. G. Kostyuk, Plasticity and Fracture of a Crystal Material Subjected to Complex
Loading [in Russian], Izd-vo MEI, Moscow, 2000. |
| 19. | D. Kolarov, A. Baltov, and N. Boncheva, Mechanics of Plastic Media [Russian translation],
Mir, Moscow, 1979. |
| 20. | Yu. N. Rabotnov, Creep in Structural Members [in Russian], Nauka, Moscow, 1966. |
| 21. | V. V. Novozhilov and Yu. I. Kadashevich, Microstresses in Structural Materials,
Mashinostroenie, Leningrad, 1990. |
|
| Received |
17 September 2002 |
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