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Effect of Thermo-Mechanical Coupling and Large Deformation on the Response of SMA Structures

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Vibration Engineering and Technology of Machinery, Volume I (VETOMAC 2021)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 137))

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Abstract

This exposition presents a thermomechanical analysis of Shape Memory Alloy structures by taking into account large strain and thermomechanical coupling. The Total Lagrangian (TL) approach is utilized to implement the thermodynamically consistent constitutive model of Lagoudas et al. (Int J Plast 16:1309–1343, [1]) in a non-linear finite element (FE) framework. Using the Newton-Raphson (NR) iterative approach, the mechanical and thermal equilibrium equations are solved concurrently while taking into account the coupling factors, i.e. the latent heat of phase transformation and the thermoelastic heat. Coupled pseudoelastic analysis and thermal recovery of an SMA plate with a hole are performed to explore the capability of the developed finite element formulation. A delayed response occurs during transformation as a result of the introduction of the heat equation with the thermomechanical coupling factors; thus playing a significant contribution in determining the response of SMA structures subjected to thermomechanical loading.

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References

  1. Qidwai M, Lagoudas D. On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material. Int J Plast. 2000;16(10–11):1309–43.

    Article  MATH  Google Scholar 

  2. Machado L, Savi M. Medical applications of shape memory alloys. Braz J Med Biol Res. 2003;36(6):683–91.

    Article  Google Scholar 

  3. Hartl DJ, Lagoudas DC. Aerospace applications of shape memory alloys. Proc Instit Mech Eng Part G J Aerosp Eng. 2007;221(4):535–52.

    Article  Google Scholar 

  4. Song G, Ma N, Li HN. Applications of shape memory alloys in civil structures. Eng Struct. 2006;28(9):1266–74.

    Article  Google Scholar 

  5. Hackl K, Heinen R, Schmahl WW, Hasan M. Experimental verification of a micromechanical model for polycrystalline shape memory alloys in dependence of martensite orientation distributions. Mater Sci Eng A. 2008;481:347–50.

    Article  Google Scholar 

  6. Levitas VI, Ozsoy IB. Micromechanical modeling of stress-induced phase transformations: part 1 thermodynamics and kinetics of coupled interface propagation and reorientation. Int J Plast. 2009;25(2):239–280.

    Google Scholar 

  7. Tanaka K. A thermomechanical sketch of shape memory effect; one dimensional tensile behavior. Int J Numer Meth Eng. 1986;18:251–63.

    Google Scholar 

  8. Liang C, Rogers CA. One-dimensional thermomechanical constitutive relations for shape memory materials. J Intell Mater Syst Struct. 1990;2:207–34.

    Article  Google Scholar 

  9. Brinson LC. One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J Intell Mater Syst Struct. 1993;4:229–42.

    Article  Google Scholar 

  10. Boyd JG, Lagoudas DC. A thermodynamical constitutive model for shape memory materials. Int J Plast. 1996;12:805–42.

    Article  MATH  Google Scholar 

  11. Birman V. Review of mechanics of shape memory alloy structures. Appl Mech Rev. 1997;50(11):629–45.

    Article  Google Scholar 

  12. Lagoudas DC, Entchev PB, Popov P, Patoor E, Brinson LC, Gao X. Shape memory alloys, part ii: modeling of polycrystals. Mech Mater. 2006;38(5–6):430–62.

    Article  Google Scholar 

  13. Paiva A, Savi MA. An overview of constitutive models for shape memory alloys. Math Probl Eng. 2006;2006.

    Google Scholar 

  14. Patoor E, Lagoudas DC, Entchev PB, Brinson LC, Gao X. Shape memory alloys, part I: general properties and modeling of single crystals. Mech Mater. 2006;38(5–6):391–429.

    Article  Google Scholar 

  15. Khandelwal A, Buravalla V. Models for shape memory alloy behavior: an overview of modeling approaches. Int J Struct Changes Solids. 2009;1(1):111–48.

    Google Scholar 

  16. Abaqus I. ABAQUS theory manual. RI: Providence; 2003.

    Google Scholar 

  17. Tabesh M, Lester B, Hartl D, Lagoudas D. Influence of the latent heat of transformation and thermomechanical coupling on the performance of shape memory alloy actuators. In: Smart materials, adaptive structures and intelligent systems, vol. 45103. American Society of Mechanical Engineers; 2012. p. 237–248.

    Google Scholar 

  18. Thiebaud F, Collet M, Foltete E, Lexcellent C. Implementation of a multi-axial pseudoelastic model to predict the dynamic behavior of shape memory alloys. Smart Mater Struct. 2007;16(4):935.

    Article  Google Scholar 

  19. Yang SB, Xu M. Finite element analysis of 2D SMA beam bending. Acta Mech Sin. 2011;27(5):738.

    Article  MATH  Google Scholar 

  20. Seelecke S, Muller I. Shape memory alloy actuators in smart structures: modeling and simulation. Appl Mech Rev. 2004;57(1):23–46.

    Article  Google Scholar 

  21. Alipour A, Kadkhodaei M, Ghaei A. Finite element simulation of shape memory alloy wires using a user material subroutine: parametric study on heating rate, conductivity, and heat convection. J Intell Mater Syst Struct. 2015;26(5):554–72.

    Article  Google Scholar 

  22. Solomou AG, Machairas TT, Saravanos DA. A coupled thermomechanical beam finite element for the simulation of shape memory alloy actuators. J Intell Mater Syst Struct. 2014;25(7):890–907.

    Article  Google Scholar 

  23. Solomou AG, Machairas TT, Saravanos DA, Hartl DJ, Lagoudas DC. A coupled layered thermomechanical shape memory alloy beam element with enhanced higher order temperature field approximations. J Intell Mater Syst Struct. 2016;27(17):2359–84.

    Article  Google Scholar 

  24. Solomou AG, Machairas TT, Karakalas AA, Saravanos DA. Co-rotational thermo-mechanically coupled multi-field framework and finite element for the large displacement analysis of multi-layered shape memory alloy beam-like structures. Smart Mater Struct. 2017;26(6): 065028.

    Google Scholar 

  25. Kundu A, Banerjee A. Coupled thermomechanical modelling of shape memory alloy structures undergoing large deformation. Int J Mech Sci. 2022;220:107102.

    Google Scholar 

  26. Bathe KJ, Ramm E, Wilson EL. Finite element formulations for large deformation dynamic analysis. Int J Numer Meth Eng. 1975;9(2):353–86.

    Article  MATH  Google Scholar 

  27. Bangerth W, Hartmann R, Kanschat G. Deal II—a general purpose object oriented finite element library. ACM Trans Math Softw. 2007;33(4):24/1–24/27.

    Google Scholar 

  28. Arndt D, Bangerth W, Clevenger TC, Davydov D, Fehling M, Garcia-Sanchez D et al. The deal II library, version 9.1. J Numer Math. 2019;27(4):203–213.

    Google Scholar 

  29. Qidwai MA, Lagoudas DC. Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms. Int J Numer Meth Eng. 2000;47:1123–68.

    Article  MATH  Google Scholar 

  30. Bathe KJ. Finite element procedures. Klaus-Jurgen Bathe; 2006.

    Google Scholar 

  31. Crank J, Nicolson P. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. In: Mathematical proceedings of the Cambridge philosophical society, vol. 43. Cambridge University Press; 1947. p. 50–67.

    Google Scholar 

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Acknowledgements

The Department of Mechanical Engineering at IIT Guwahati, and project sponsored by SERB, SERB/CRG/2020/003585, are acknowledged and thanked by the authors for providing the essential resources.

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Authors and Affiliations

  1. Department of Mechanical Engineering, IIT Guwahati, Assam, India

    Animesh Kundu & Atanu Banerjee

Authors
  1. Animesh Kundu
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  2. Atanu Banerjee
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Correspondence to Animesh Kundu .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, India

    Rajiv Tiwari

  2. Department of Mechanical Engineering, B.M.S. College of Engineering, Bengaluru, Karnataka, India

    Y. S. Ram Mohan

  3. Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India

    Ashish K. Darpe

  4. Department of Mechanical Engineering, B.M.S. College of Engineering, Bengaluru, Karnataka, India

    V. Arun Kumar

  5. Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna, Bihar, India

    Mayank Tiwari

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Kundu, A., Banerjee, A. (2023). Effect of Thermo-Mechanical Coupling and Large Deformation on the Response of SMA Structures. In: Tiwari, R., Ram Mohan, Y.S., Darpe, A.K., Kumar, V.A., Tiwari, M. (eds) Vibration Engineering and Technology of Machinery, Volume I. VETOMAC 2021. Mechanisms and Machine Science, vol 137. Springer, Singapore. https://doi.org/10.1007/978-981-99-4721-8_12

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  • DOI: https://doi.org/10.1007/978-981-99-4721-8_12

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-4720-1

  • Online ISBN: 978-981-99-4721-8

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