 | | 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 |
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| I. S. Nikitin, "Constitutive equations of the elastoviscoplastic model and slip theory," Mech. Solids. 42 (2), 260-270 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
2 |
Pages |
260-270 |
| Title |
Constitutive equations of the elastoviscoplastic model and slip theory |
| Author(s) |
I. S. Nikitin (Moscow State Aviation Technological University, Orshanskaya 3, Moscow, 121552, Russia, i_nikitin@list.ru) |
| Abstract |
On the basis of ideas of the Batdorf-Budiansky slip theory, we construct a model of an elastoviscoplastic medium. The slip conditions on the unit area take into account the fact that the tangential stresses depend on the slip velocity but are close to the dry friction conditions for small viscosity. Under certain assumptions, we manage to integrate the plastic shear rate over all possible slip areas in the case of an arbitrary three-dimensional stress state and obtain an expression for the plastic strain rate tensor. |
| References |
| 1. | S. B. Batdorf and B. Budyanskii,
"Mathematical Theory of Plasticity Based on the Concept of Slip,"
in Mechanics [Russian translation of foreign papers],
No. 1, 135-155 (1962). |
| 2. | W. T. Koiter,
"The Relations Between Stresses and Strains. Variational Theorems
and Uniqueness Theorems for Elastoplastic Materials with a
Singular Yield Surface,"
in Mechanics [Russian translation of foreign papers],
No. 2, 117-129 (1960). |
| 3. | I. V. Knets,
Basic Modern Trends in the Mathematical Theory of Plasticity
(Zinatne, Riga, 1971)
[in Russian]. |
| 4. | N. Yu. Shvailo,
"To the Theory of Plasticity Based on the Concept of Slip,"
Prikl. Mekhanika
12 (11), 12-24 (1976). |
| 5. | A. K. Malmeister,
"Foundations of the Theory of Local Strains,"
Mekh. Polimer.,
No. 4, 12-27 (1965). |
| 6. | A. N. Mokhel, R. L. Salganik, and S. A. Khristianovich, "On
Plastic Strain of Strengthening Metals and Alloys. Constitutive
Equations and Calculations According to Them," Izv. Akad. Nauk
SSSR. Mekh. Tverd. Tela, No. 4, 119-141 (1983) [Mech. Solids
(Engl. Transl.)]. |
| 7. | I. S. Nikitin,
Dynamics of Layered and Block Media with Slip and Friction.
Preprint No. 366, IPMekh RAN (Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 1989)
[in Russian]. |
| 8. | I. S. Nikitin,
"On Wave Propagation in Layered and Block Media with Friction
on the Contact Boundaries,"
Izv. Akad. Nauk SSSR. Fiz. Zemli,
No. 7, 3-11 (1989). |
| 9. | P. Perzyna,
Fundamental Problems in Viscoplasticity
(Mir, Moscow, 1968)
[in Russian]. |
| 10. | V. N. Kukudzhanov, Propagation of Elastoplastic Waves in Rods
with Strain Rate Influence Taken into Account (Computer Center, AN
SSSR, Moscow, 1967) [in Russian]. |
|
| Received |
21 December 2005 |
| Link to Fulltext |
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