Skip to main content
Log in

Two-Way Coupled Statement of the Problem of Loss of Stability due to Inverse Thermoelastic Phase Transition in a Shape Memory Alloy

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

A two-way coupled statement of stability problem for shape memory alloy elements is given in the framework of the “fixed load” and “variable load” concepts. It is shown that the largest values of the critical parameters are obtained when solving the problem in the two-way coupled statement in the framework of the “fixed load” concept and the least values are obtained in the oneway coupled statement in the framework of the “variable load” concept.

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. M. A. Rahman, J. Qui, and J. Tani, “Buckling and Postbuckling Characteristics of the Superelastic SMA Columns,” Int. J. Solids Struct. 38, 9253–9265 (2001).

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  3. M. A. Rahman and J. Tani, “Postbuckling Characteristics of the Short Superelastic Shape Memory Alloy Columns – Experiment and Quantitative Analysis,” Int. J. Appl.Mech. Engng 11 (4), 941–955 (2006).

    Google Scholar 

  4. M. A. Rahman, S. R. Akanda, and M. A. Hossain, “Effect of Cross Section Geometry on the Response of an SMA Column,” J. Intell.Mater. Syst. Struct. 19 (2), 243–252 (2008).

    Article  Google Scholar 

  5. S. Nemat-Nasser, J. Y. Choi, J. B. Isaacs, and D.W. Lisher, “ExperimentObservation ofHigh-Rate Buckling of Thin Cylindrical Shape Memory Shells,” in SPIE Proc.: Smart Structure and Materials 2005. Active Materials: Behavior and Mechanics, Ed. by W. D. Armstrong, Vol. 5761 (2005), pp. 347–354.

    ADS  Google Scholar 

  6. M. R. Amini and S. Nemat-Nasser, “Dynamic Buckling and Recovery of Thin Cylindrical Shells,” in SPIE Proc.: Smart Structure and Materials 2005. Active Materials: Behavior and Mechanics, Ed. by W. D. Armstrong, Vol. 5761 (2005), pp. 450–453.

    ADS  Google Scholar 

  7. S. Nemat-Nasser, J. Y. Choi, J. B. Isaacs, and D. W. Lisher, “Quasi-Static and Dynamic Buckling of Thin Cylindrical ShapeMemory Alloy Shells,” J. Appl.Mech. 73 (5), 825–833 (2006).

    Article  ADS  Google Scholar 

  8. A. Tang and D. Li, “Quasi-Static Axial Buckling of TiNi Thin-Walled Cylindrical Shells,” Thin-Walled Struct. 51, 130–138 (2012).

    Article  Google Scholar 

  9. A. Tang and D. Li, “Experimental Investigation of Axial Impact Buckling Response of Pseudo-Elastic NiTi Cylindrical Shells,” Int. J. Impact Engng 39, 28–41 (2012).

    Article  Google Scholar 

  10. D. Jiang, N. Bechle, C. M. Landis, and S. Kyriakides, “Buckling and Recovery of NiTi Tubes under Axial Compression,” Int. J. Solids Struct. 80, 52–63 (2016).

    Article  Google Scholar 

  11. P. A. Michailidis, N. Triantafyllidis, J. A. Shaw, and D. S. Grummon, “Superelasticity and Stability of a Shape Memory Alloy Hexagonal Honeycomb under In-Plane Compression,” Int. J. Solids Struct. 46, 2724–2738 (2009).

    Article  MATH  Google Scholar 

  12. F. Richter, O. Kastner, and G. Eggeler, “Finite-Element Simulation of the Anti-Buckling-Effect of a Shape Memory Alloy Bar,” J.Mater. Engng Perform. 20 (4-5), 719–730 (2011).

    Article  Google Scholar 

  13. J.Ocel,R.DesRoches,R. T. Leon, et al., “Steel Beam– Column Connections Using Shape Memory Alloys,” J. Struct. Engng 130 (5), 739–740 (2004).

    Google Scholar 

  14. R. T. Leon, R. DesRoches, J. Ocel, and G. Hess, “Innovative Beam Column Using Shape Memory Alloys,” in SPIE Proc.: Smart Structure and Materials 2001. Smart System for Bridges, Structures, and Highways, Ed. by S. C. Liu, Vol. 4330 (2001), pp. 227–237.

    ADS  Google Scholar 

  15. A. A. Movchan, L. G. Silchenko, S. A. Kazarina, et al., “Stability of Titanium Nickelide Rods Loaded in theMode ofMartensite Inelasticity,” Probl. Mashinostr. Nadezhn.Mashin, No. 3, 72–80 (2012) [J.Machin. Manufact. Reliabil. (Engl. Transl.) 41 (3), 245–251 (2012)].

    Google Scholar 

  16. Y. Urushiyama, D. Lewinnek, J. Qui, 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. Engng 46 (1), 60–67 (2003).

    Google Scholar 

  17. J. Kunavar, F. Kosel, A. Pukšič, and T. Videnič, “GeometryOptimization in Buckling of ShapeMemory Alloy Column due to Constrained Recovery,” J. Intell.Mater. Syst. Struct. 23 (1), 65–76 (2012).

    Article  Google Scholar 

  18. 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)].

    Google Scholar 

  19. M. A. Savi, P.M. C. L. Pachco, and A.M. B. Braga, “Chaos in a Shape Memory Two-Bar Truss,” Int. J. Non-Lin.Mech. 37 (8), 1387–1395 (2002).

    Article  MATH  Google Scholar 

  20. J. J. Lee and S. Choi, “Thermal Buckling and Postbuckling Analysis of a Laminated Composite Beam with Embedded SMA Actuators,” Compos. Struct. 47 (1-4), 695–703 (1999).

    Article  Google Scholar 

  21. A. A. Movchan and S. A. Kazarina, “Experimental Study of Stability Loss Phenomenon due to Thermoelastic Phase Transformations under the Action of Compressing Stresses,” Probl. Mashinostr. Nadezhn. Mashin, No. 6, 82–89 (2002).

    Google Scholar 

  22. A. A. Movchan and L. G. Sil’chenko, “Buckling of a Rod Undergoing Direct or Inverse 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)].

    MATH  Google Scholar 

  23. A. A. Movchan and L. G. Sil’chenko, “Analysis of Buckling Induced by the Direct Thermoelastic Transformation under the Action of Compression Stresses,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 132–144 (2004) [Mech. Solids (Engl. Transl.) 39 (2), 104–114 (2004)].

    Google Scholar 

  24. 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)].

    MATH  Google Scholar 

  25. 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. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 164–178 (2004) [Mech. Solids (Engl. Transl.) 39 (5), 134–145 (2004)].

    Google Scholar 

  26. 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. Transl.) 70 (5), 785–795 (2006)].

    MathSciNet  MATH  Google Scholar 

  27. A. A. Movchan, “Selecting a Phase-DiagramApproximation and aModel of theDisappearance 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)].

    Google Scholar 

  28. A. A. Movchan and L. G. Sil’chenko, “Buckling of a Circular Plate Made of a Shape Memory Alloy due to a Inverse Thermoelastic Martensite Transformation,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 117–130 (2008) [Mech. Solids (Engl. Transl.) 43 (1), 100–111 (2008)].

    Google Scholar 

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

    MATH  Google Scholar 

  30. L. I. Shkutin, “Analysis of Plane Phase Strains of Rods and Plates,” Zh. Prikl. Mekh. Tekhn. Fiz. 47 (2), 156–164 (2006) [J. Appl.Mech. Tech. Phys. (Engl. Transl.) 47 (2), 282–288 (2006)].

    MATH  Google Scholar 

  31. 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)].

    MATH  Google Scholar 

  32. 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,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 137–147 (2010) [Mech. Solids (Engl. Transl.) 45 (6), 876–884 (2010)].

    MATH  Google Scholar 

  33. L.G. Sil’chenko, A. A. Movchan, and I.A. Movchan, “Structural Transformation Taken into Account during the Analysis of the Stability of a Round Plate with Shape Memory,” Probl. Mashinostr. Nadezhn. Mashin, No. 5, 57–65 (2010) [J. Machin.Manufact. Reliabil. (Engl. Transl.) 39 (5), 452–458 (2010)].

    Google Scholar 

  34. I. V. Mishustin and A. A. Movchan, “Modeling of Phase and Structure Transformations Occurring in Shape MemoryAlloys under NonmonotonicallyVarying Stresses,” Izv. Ross. Akad.Nauk.Mekh. Tverd. Tela, No. 1, 37–53 (2014) [Mech. Solids (Engl. Transl.) 49 (1), 27–39 (2014)].

    Google Scholar 

  35. I. V. Mishustin and A. A. Movchan, “Analog of the Plastic Flow Theory for DescribingMartensitic Inelastic Strains in Shape Memory Alloys,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 78–95 (2015) [Mech. Solids (Engl. Transl.) 50 (2), 176–190 (2015)].

    Google Scholar 

  36. F. Shanley, “Column Theory beyond the Elastic Limit,” Mekh., No. 2, 88–98 (1951).

    Google Scholar 

  37. Ya. G. Panovko and I. I. Gubanova, Stability and Vibrations of Elastic Systems (Nauka, Moscow, 1987) [in Russian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Movchan.

Additional information

Original Russian Text © S.A. Dumanskii, A.A. Movchan, 2017, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2017, No. 5, pp. 37–48.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dumanskii, S.A., Movchan, A.A. Two-Way Coupled Statement of the Problem of Loss of Stability due to Inverse Thermoelastic Phase Transition in a Shape Memory Alloy. Mech. Solids 52, 501–510 (2017). https://doi.org/10.3103/S0025654417050053

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654417050053

Keywords

Navigation