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Abnormal Buckling of Thin-Walled Bodies with Shape Memory Effects Under Thermally Induced Phase Transitions

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Recent Developments in the Theory of Shells

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 110))

Abstract

Buckling and postbuckling of thin-walled structures made from the Nickel-Titanium shape memory alloy and undergoing non-isothermal direct martensite transitions under varying temperatures are simulated. The once coupled Movchan’s model of thermo-elastic shape memory alloy behavior is represented in the incremental formulation for the use within numerical algorithms of nonlinear solid mechanics. The equilibrium state’s bifurcation is studied on the background of Lyapunov’s stability concept. The physically and geometrically nonlinear solid model allows one to study the martensite phase distribution over the cross-section as well as along the structure during its’ buckling and postbuckling deforming. It is shown that the direct martensite transition induced by temperature changes and heterogeneous stress fields in compressed prismatic beams with initial imperfections causes the buckling phenomenon. The obtained results are consistent with the analytical predictions of A.Movchan and L.Silchenko assuming the supplementary phase transform occurring everywhere in accordance with the extended Shenley concept. Thus, the fundamental assumption about decisive contribution of martensite phase transitions in the buckling of thin-walled structures of shape memory alloys is vindicated.

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Acknowledgements

This investigation was performed under the State Task for Basic Researches (register number AAAA-A19-119012290118-3), state register number AAAA-A17-117032010136-3 and partially supported by the Russian Foundation for Basic Researches under grant Nr. 19-01-00695\(\_\)a.

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Authors and Affiliations

  1. PAO Severstal, 127299, Klara Zetkin ul. 2, Moscow, Russia

    Dmitry V. Nushtaev

  2. Institute of Applied Mechanics of Russian Academy of Sciences, 125040, Leningradskiy prosp. 7, Moscow, Russia

    Sergey I. Zhavoronok

Authors
  1. Dmitry V. Nushtaev
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  2. Sergey I. Zhavoronok
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Correspondence to Sergey I. Zhavoronok .

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Editors and Affiliations

  1. Faculty of Mechanical Engineering, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Jacek Chróścielewski

  3. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Victor A. Eremeyev

  4. Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

    Krzysztof Wiśniewski

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Nushtaev, D.V., Zhavoronok, S.I. (2019). Abnormal Buckling of Thin-Walled Bodies with Shape Memory Effects Under Thermally Induced Phase Transitions. In: Altenbach, H., Chróścielewski, J., Eremeyev, V., Wiśniewski, K. (eds) Recent Developments in the Theory of Shells . Advanced Structured Materials, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-030-17747-8_26

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