Skip to main content
Log in

Solution of The Double-Coupled Problem of Buckling of a Shape Memory Alloy Rod Due to The Direct Thermoelastic Phase Transformation

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Problems of the stability of a shape memory alloy rod during the direct martensitic phase transformation under constant compressive loading are solved taking into account the effect of stresses on the phase transition and the effect of the phase transition on the temperature regime using various statements. A comparison of the results of the obtained solutions is made.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. A. Movchan and S. A. Kazarina, “Experimental Investigation of the Buckling Caused by Thermoelastic Phase Transformations under the Action of Compressive Stresses,” Probl. Mashinostr. Nadezh. Mashin, No. 6, 82–89 (2002).

    Google Scholar 

  2. A. A. Movchan, I. A. Movchan, and L. G. Sil’chenko, “Influence of Structural Transformation and the Nonlinearity of the Deformation Process on the Stability of a Shape Memory Alloy Rod,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 6, pp. 137–147 (2010).

    Google Scholar 

  3. M. A. Rahman, J. Qui, and J. Tani, “Buckling and Postbuckling Characteristics of the Superelastic SMA Columns—Numerical Simulation,” J. Intell. Mater. Syst. Struct. 16, 691–702 (2005).

    Article  Google Scholar 

  4. Z. Tang and D. Li, “Quasi-Static Axial Buckling Behavior of TiNi Thin-Walled Cylindrical Shells,” Thin-Walled Structures 51, 130–138 (2012).

    Article  Google Scholar 

  5. A. A. Movchan, L. G. Sil’chenko, S. A. Kazarina, etc., “Stability of Titanium Nickelide Rods Loaded in the Martensitic Inelasticity Regime,” Probl. Mashinostr. Nadezh. Mashin, No. 3, 72–80 (2012).

    Google Scholar 

  6. Y. Urushiyamaa, D. Lewinnek, J. Qiau, and J. Tani, “Buckling of Shape Memory Alloy Columns: Buckling of Curved Column and Twinning Deformation Effect,” JMSE Int. J., Ser. A: Solid Mech. Mater. Eng. 46 (1), 60–67 (2003).

    Article  Google Scholar 

  7. J. Kunavar, F. Kozel, A. Puksic, and T. Videnic, “Geometry Optimization in Buckling of Shape Memory Alloy Columns Due to Constrained Recovery,” J. Intell. Mater. Syst. Struct. 23, 65–76 (2012).

    Article  Google Scholar 

  8. G. A. Malygin, “Euler Instability of the Bidirectional Shape Memory Effect in a Titanium Nickelide Strip,” Fiz. Tverd. Tela 45 (12), 2233–2237 (2003).

    Google Scholar 

  9. A. A. Movchan and L. G. Sil’chenko, “Buckling of a Rod Undergoing Direct or Reverse Martensite Transformation under Compressive Stresses,” Prikl. Mekh. Tekh. Fiz. 44 (3), 169–178 (2003) [J. Appl. Mech. Tech. Phys. 44 (3), 442–449 (2003)].

    MATH  Google Scholar 

  10. A. A. Movchan an 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).

    MATH  Google Scholar 

  11. A. A. Movchan and L. G. Sil’chenko, “The stability of a Circular Plate of a Shape Memory Alloy during a Direct Martensitic Transformation,” Prikl. Mat. Mekh. 70 (5), 871–883 (2006).

    MathSciNet  Google Scholar 

  12. A. A. Movchan, I. A. Movchan, and L. G. Sil’chenko, “Stability of an Annular Plate of a Shape Memory Alloy,” Prikl. Mekh. Tekh. Fiz. 52 (2), 144–155 (2007) [J. Appl. Mech. Tech. Phys. 52 (2), 279–287 (2011)].

    MATH  Google Scholar 

  13. L. I. Shkutin, “Analysis of Axisymmetric Phase Strains in Plates and Shells,” Prikl. Mekh. Tekh. Fiz. 48 (2), 163–171 (2007) [J. Appl. Mech. Tech. Phys. 48 (2), 285–291 (2007)].

    MATH  Google Scholar 

  14. I. V. Mishustin and A. A. Movchan, “Modeling of Phase and Structure Transformations Occurring in Shape Memory Alloys under Nonmonotonically Varying Stresses,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 1, 37–53 (2014).

    Google Scholar 

  15. I. V. Mishustin and A. A. Movchan, “Analog of the Plastic Flow Theory for Describing Martensitic Inelastic Strains in Shape Memory Alloys,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 78–95 (2015).

    Google Scholar 

  16. S. I. Zhavoronok and D. V. Nushtaev, “Solving Problems of Buckling and Supercritical Deformation of a Shape Memory Effect Rod during Phase Transition,” in Mechanics of Composite Materials and Structures and Complex and Heterogeneous Media, Proc. of the All-Russian Conf., Moscow, November 21–23, 2017 (Inst. of Appl. Mech. of the Russian Academy of Sciences, Moscow, 2017), pp. 86–90.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Movchan.

Additional information

Original Russian Text © A.A. Movchan, S.A. Dumanskii.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 4, pp. 160–168, July–August, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Movchan, A.A., Dumanskii, S.A. Solution of The Double-Coupled Problem of Buckling of a Shape Memory Alloy Rod Due to The Direct Thermoelastic Phase Transformation. J Appl Mech Tech Phy 59, 716–723 (2018). https://doi.org/10.1134/S0021894418040193

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021894418040193

Keywords

Navigation