 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A.A. Movchan, I.A. Movchan, and L.G. Sil'chenko, "Effect of Structural Transformation and Deformation Nonlinearity on the Stability of a Shape Memory Alloy Rod," Mech. Solids. 45 (6), 876-884 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
6 |
Pages |
876-884 |
| DOI |
10.3103/S0025654410060117 |
| Title |
Effect of Structural Transformation and Deformation Nonlinearity on the Stability of a Shape Memory Alloy Rod |
| Author(s) |
A.A. Movchan (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia, movchan47@mail.ru)
I.A. Movchan (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia)
L.G. Sil'chenko (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia, seliger@mail.ru) |
| Abstract |
Within the framework of a model of nonlinear deformations
of shape memory alloys (SMA) under phase and structural transformations and for different statements of the problem,
an analytical solution of the problem of stability
of an SMA rod undergoing a direct martensitic phase transformation under the action of a compressive load is obtained. It is shown that taking account of the nonlinearity of the deformation process and structural transformation in the transition into the adjacent form of equilibrium significantly changes the solution for sufficiently flexible rods. At the same time, taking into account the strains developed in a phase transition is topical for thick-walled SMA elements. |
| Keywords |
shape memory, stability, phase transition, structural transformation, nonlinearity, rod |
| References |
| 1. | A. A. Movchan and I. A. Movchan,
"One-Dimensional Micromechanical Model of Nonlinear Deformation of Shape Memory Alloys
under Direct and Inverse Thermoelastic Transformations,"
Mekh. Komp. Mater. Konstr.
13 (3), 297-322 (2007)
[J. Comp. Mech. Design (Engl. Transl.)]. |
| 2. | A. A. Movchan and I. A. Movchan,
"Model of Nonlinear Deformation of Shape Memory Alloys in Active Processes
of Direct and Structure Transformations,"
Mekh. Komp. Mater. Konstr.
14 (1), 75-87 (2008)
[J. Comp. Mech. Design (Engl. Transl.)]. |
| 3. | A. A. Movchan, I. A. Movchan, and L. G. Sil'chenko,
"Micromechanical Model of Nonlinear Deformation of Shape Memory Alloys under Phase and Structure Transitions,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 118-130 (2010)
[Mech. Solids (Engl. Transl.)
45 (3), 406-416 (2010)]. |
| 4. | A. A. Movchan and S. A. Kazarina,
"Experimental Investigation of the Effect of Buckling Caused by Thermoelastic Phase
Transformations under the Action of Compressive Stresses,"
Probl. Mashinostr. Nadezhn. Mashin,
No. 6, 82-89 (2002). |
| 5. | A. A. Movchan and L. G. Sil'chenko,
"Buckling of a Rod Undergoing Direct or Reverse Martensite
Transformation under Compressive Stresses,"
Zh. Prikl. Mekh. Tekhn. Fiz.
44 (3), 169-178 (2003)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
44 (3), 442-449 (2003)]. |
| 6. | A. A. Movchan and L. G. Sil'chenko,
"Analysis of Buckling Induced by the Direct Thermoelastic Transformation under the Action of Compression Stresses,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 132-144 (2004)
[Mech. Solids (Engl. Transl.)
39 (2), 104-114 (2004)]. |
| 7. | A. A. Movchan and L. G. Sil'chenko,
"The Stability of a Plate of Shape-Memory Alloy in a Direct Thermoelastic Phase Transition,"
Prikl. Mat. Mekh.
68 (1), 60-72 (2004)
[J. Appl. Math. Mech. (Engl. Transl.)
68 (1), 53-64 (2004)]. |
| 8. | A. A. Movchan and L. G. Sil'chenko,
"Analytical Solution of the Coupled Buckling Problem for a Plate From a Shape Memory
Alloy Subjected to Inverse Martensite Transformation,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 164-178 (2004)
[Mech. Solids (Engl. Transl.)
39 (5), 134-145 (2004)]. |
| 9. | A. A. Movchan and L. G. Sil'chenko,
"The Stability of a Circular Plate of Shape Memory Alloy during a Direct Martensite Transformation,"
Prikl. Mat. Mekh.
70 (5), 871-883 (2006)
[J. Appl. Math. Mech. (Engl. Tranl.)
70 (5), 785-795 (2006)]. |
| 10. | A. A. Movchan and L. G. Sil'chenko,
"Buckling of a Circular Plate Made of a Shape Memory Alloy due to a Reverse Thermoelastic Martensite Transformation,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 117-130 (2008)
[Mech. Solids (Engl. Transl.)
43 (1), 100-111 (2008)]. |
| 11. | M. A. Khusainov,
"Investigation of the Axisymmetric Buckling of Round Plates,"
Zh. Tekhn. Fiz.
67 (6), 118-120 (1997)
[Tech. Phys. (Engl. Transl.)
42 (6), 692-694 (1997)]. |
| 12. | G. A. Malygin,
"Euler Instability of Bidirectional Shape Memory Effect in a Titanium Nickelide Strip,"
Fiz. Tverd. Tela
45 (12), 2233-2237 (2003)
[Phys. Solid State (Engl. Transl.)
45 (12), 2342-2347 (2003)]. |
| 13. | G. A. Malygin and M. A. Khusainov,
"Stability of the Mechanical Behavior of an Arched TiNi Strip under the Conditions of the Constrained Shape Memory Effect,"
Zh. Tekhn. Fiz.
74 (10), 57-63 (2004)
[Tech. Phys. (Engl. Transl.)
49 (10), 1301-1307 (2004)]. |
| 14. | L. I. Shkutin,
"Analysis of Axisymmetric Phase Strains in Plates and Shells,"
Zh. Prikl. Mekh. Tekhn. Fiz.
48 (2), 163-171 (2007)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
48 (2), 285-291 (2007)]. |
| 15. | L. I. Shkutin,
"Axisymmetric Deformation of Plates and Shells with Phase Trasformations under Thermal Cycling,"
Zh. Prikl. Mekh. Tekhn. Fiz.
49 (2), 204-210 (2008)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
49 (2), 330-335 (2008)]. |
| 16. | A. A. Movchan,
"Micromechanical Constitutive Equations for Shape Memory Alloys,"
Probl. Mashinostr. Nadezhn. Mashin,
No. 6, 47-53 (1994). |
| 17. | A. A. Movchan,
"Micromechanical Description of the Deformation due to Martensite Transformations in Shape-Memory Alloys,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 197-205 (1995)
[Mech. Solids (Engl. Transl.)
30 (1), 186-192 (1995)]. |
| 18. | A. A. Movchan,
"Selecting a Phase-Diagram Approximation and a Model of the Disappearance
of Martensite Crystals for Shape Memory Alloys,"
Zh. Prikl. Mekh. Tekhn. Fiz.
36 (2), 173-181 (1995)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
36 (2), 300-307 (1995)]. |
| 19. | G. A. Malygin,
"Theory of Diffuse Martensitic Phase Transitions in Ferroelastics and Shape-Memory Alloys,"
Fiz. Tverd. Tela
36 (5), 1489-1501 (1994)
[Phys. Solid State (Engl. Transl.)
36 (5), 815-820 (1994)]. |
| 20. | A. A. Movchan and Nyunt Soe,
"Thermodynamic Description of Shape Memory Alloy Behavior Using the
Gibbs Additive Potential,"
Zh. Prikl. Mekh. Tekhn. Fiz.
47 (4), 98-103 (2006)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
47 (4), 542-546 (2006)]. |
|
| Received |
12 July 2010 |
| Link to Fulltext |
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