 | | 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
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| In English (Mech. Solids): | | 4811 |
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| I. S. Nikitin, "Elastoplastic model and theory of slipping for the three-dimensional stress state," Mech. Solids. 44 (3), 480-489 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
3 |
Pages |
480-489 |
| DOI |
10.3103/S0025654409030170 |
| Title |
Elastoplastic model and theory of slipping for the three-dimensional stress state |
| Author(s) |
I. S. Nikitin (Moscow State Aviation Technological University, Orshanskaya 3, Moscow, 121552 Russia, i_nikitin@list.ru) |
| Abstract |
On the basis of concepts of the Batdorf-Budyanskii theory of
slipping, we construct a model of elastoplastic medium for the case of three-dimensional stress state. The slipping conditions on the unit site take into account the local yield criterion and the local loading criterion. Under certain assumptions, one can integrate the increments of plastic shears over all possible sites of slipping in the case of an arbitrary three-dimensional stress state and obtain the constitutive relations for the elastoplastic model, which is a version of the theory of plastic flow. |
| References |
| 1. | S.B. Batdorf and B. Budiansky,
"A Mathematical Theory of Plasticity Based
on the Concept of Slip,"
in Mechanics, No. 1
(1962), pp. 135-155
[National Advisory Committee for Aeronautics-Techn. Note,
No. 1871]. |
| 2. | W.T. Koiter,
"Stress-Strain Relations, Uniqueness and Variational Theorems for Elastic Plastic
Materials with a Singular Yield Surface,"
in Mechanics, No. 2,
(1960), pp. 117-129
[Quart. Appl. Math. 11, 350-354 (1953)]. |
| 3. | V.D. Kliushnikov,
"On Plasticity Laws for Work-Hardening Materials,"
"On Plasticity Laws for Materials with Strengthening,"
Prikl. Mat. Mekh. 22 (1), 97-118 (1958)
[J. Appl. Math. Mech. (Engl. Transl.) 22 (1), 129-160 (1958)]. |
| 4. | N.Yu. Shvaiko,
"Theory of Plasticity, Based on the Concept of Slip,"
Prikl. Mekh. 12 (11), 12-24 (1976)
[Int. Appl. Mech. (Engl. Transl.) 12 (11), 1102-1112 (1976)]. |
| 5. | A.K. Malmeister,
" Basis of the Local Strains Theory (Review. 1),"
Mekh. Polimer., No. 4, 12-27 (1965)
[Polymer Mech. (Engl. Transl.) 1 (4), 7-14 (1965)]. |
| 6. | A.N. Mokhel and R.L. Salganik,
"On the Theory of Plastic Deformation of Hardening Materials,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 98-111 (1976)
[Mech. Solids (Engl. Transl.) 11 (5), 85-96 (1976)]. |
| 7. | A.N. Mokhel, R.L. Salganik, and S.A. Khristianovich,
"Plastic dEFORMATION of Strain-Hardening Metals and Alloys:
the Definition Equations and Calculations Employing Them,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 4, 119-141 (1983)
[Mech. Solids (Engl. Transl.) 18 (4), 118-139 (1983)]. |
| 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. | I.S. Nikitin,
"Constitutive Equations of the Elastoviscoplastic Model and Slip Theory,"
Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 110-122 (2007)
[Mech. Solids (Engl. Transl.) 42 (2), 260-270 (2007)]. |
| 10. | S.A. Khristianovich,
"Deformation of Strain-Hardening Plastic Material,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 2, 148-174 (1974)
[Mech. Solids (Engl. Transl.) 9 (2), 160-173 (1974)]. |
| 11. | D. Kolarov, A. Baltov, and N. Boncheva,
Mechanics of the Plastic Mediums
(Bulgarian Academy of Sciences, Sofia, 1975; Mir, Moscow, 1979) [in Bulgarian, in Russian]. |
|
| Received |
10 October 2006 |
| Link to Fulltext |
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