Skip to main content

A Shell Finite Element Model for Superelasticity of Shape Memory Alloys

  • Chapter
  • First Online:
Analysis of Shells, Plates, and Beams

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 134))

Abstract

A finite element formulation for the analysis of large strains of thin-walled shape memory alloys is briefly presented. For the shell model we use a seven-kinematic-parameter model for large deformations and rotations, which takes into account the through-the-thickness stretch and can directly incorporate a fully 3D inelastic constitutive equations. As for the constitutive model, we use a large strain isotropic formulation that is based on the multiplicative decomposition of the deformation gradient into the elastic and the transformation part and uses the transformation deformation tensor as an internal variable. Numerical examples are presented to illustrate the approach.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arghavani J, Auricchio F, Naghdabadi R, Reali A (2011) On the robustness and efficiency of integration algorithms for a 3D finite strain phenomenological SMA constitutive model. International Journal for Numerical Methods in Engineering 85(1):107–134

    Google Scholar 

  • Auricchio F (2001) A robust integration-algorithm for a finite-strain shape-memory alloy superelastic model. International Journal of Plasticity 17(7):971–990

    Google Scholar 

  • Auricchio F, Taylor RL (1997) Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior. Computer Methods in Applied Mechanics and Engineering 143(1):175–194

    Google Scholar 

  • Brank B (2005) Nonlinear shell models with seven kinematic parameters. Computer Methods in Applied Mechanics and Engineering 194(21):2336–2362

    Google Scholar 

  • Brank B (2008) Assessment of 4-node EAS-ANS shell elements for large deformation analysis. Computational Mechanics 42:39–51

    Google Scholar 

  • Brank B, Ibrahimbegovic A (2001) On the relation between different parametrizations of finite rotations for shells. Engineering Computations: Int J for Computer-Aided Engineering 18(7):950–973

    Google Scholar 

  • Brank B, Korelc J, Ibrahimbegovic A (2002) Nonlinear shell problem formulation accounting for through-the-thickness stretching and its finite element implementation. Computers & Structures 80(9):699–717

    Google Scholar 

  • Brank B, Ibrahimbegovic A, Bohinc U (2008) On prediction of 3D stress state in elastic shell by higher-order shell formulations. Comput Model Eng Sci 33:85–108, https://doi.org/10.3970/cmes.2008.033.085

  • Brojan M, Bombac D, Kosel F, Videnic T (2008) Shape memory alloys in medicine. RMZ – Materials and Geoenvironment 55:173–189

    Google Scholar 

  • CoralW, Rossi C, Colorado J, Lemus D, Barrientos A (2012) Sma-based muscle-like actuation in biologically inspired robots: A state of the art review. In: Berselli G, Vertechy R, Vassura G (eds) Smart Actuation and Sensing Systems, IntechOpen, Rijeka, chap 3

    Google Scholar 

  • Dujc J, Brank B (2012) Stress resultant plasticity for shells revisited. Computer Methods in Applied Mechanics and Engineering 247–248:146–165

    Google Scholar 

  • Evangelista V, Marfia S, Sacco E (2010) A 3D SMA constitutive model in the framework of finite strain. International Journal for Numerical Methods in Engineering 81(6):761–785

    Google Scholar 

  • Hartl DJ, Mooney JT, Lagoudas DC, Calkins FT, Mabe JH (2009) Use of a ni60ti shape memory alloy for active jet engine chevron application: II. experimentally validated numerical analysis. Smart Materials and Structures 19(1):015,021

    Google Scholar 

  • Hudobivnik B, Korelc J (2016) Closed-form representation of matrix functions in the formulation of nonlinear material models. Finite Elements in Analysis and Design 111:19–32

    Google Scholar 

  • Ibrahimbegovic A (2009) Nonlinear Solid Mechanics. Springer, Dordrecht

    Google Scholar 

  • Ibrahimbegovic A, Brank B, Courtois P (2001) Stress resultant geometrically exact form of classical shell model and vector-like parameterization of constrained finite rotations. International Journal for Numerical Methods in Engineering 52(11):1235–1252

    Google Scholar 

  • Jani JM, Leary M, Subic A, Gibson MA (2014) A review of shape memory alloy research, applications and opportunities. Materials & Design 56:1078–1113

    Google Scholar 

  • Kaneko K, Enomoto K (2011) Development of reciprocating heat engine using shape memory alloy. Journal of Environment and Engineering 6(1):131–139

    Google Scholar 

  • Korelc J, Stupkiewicz S (2014) Closed-form matrix exponential and its application in finite-strain plasticity. International Journal for Numerical Methods in Engineering 98(13):960–987

    Google Scholar 

  • Korelc J, Wriggers P (2016) Automation of Finite Element Methods. Springer

    Google Scholar 

  • Lavrencic M, Brank B (2020) Hybrid-mixed shell quadrilateral that allows for large solution steps and is low-sensitive to mesh distortion. Computational Mechanics 65:177–192

    Google Scholar 

  • McDonald Schetky L (1991) Shape memory alloy applications in space systems. Materials & Design 12(1):29 – 32

    Google Scholar 

  • Petrini L, Migliavacca F (2011) Biomedical applications of shape memory alloys. Journal of Metallurgy 2011:ID 501,483

    Google Scholar 

  • Reese S, Christ D (2008) Finite deformation pseudo-elasticity of shape memory alloys – Constitutive modelling and finite element implementation. International Journal of Plasticity 24(3):455–482

    Google Scholar 

  • Sofla AYN, Meguid SA, Tan KT, Yeo WK (2010) Shape morphing of aircraft wing: Status and challenges. Materials & Design 31(3):1284–1292

    Google Scholar 

  • Souza AC, Mamiya EN, Zouain N (1998) Three-dimensional model for solids undergoing stress-induced phase transformations. European Journal of Mechanics-A/Solids 17(5):789–806

    Google Scholar 

  • Stanic A, Brank B (2017) A path-following method for elasto-plastic solids and structures based on control of plastic dissipation and plastic work. Finite Elements in Analysis and Design 123:1–8

    Google Scholar 

  • Stupkiewicz S, Petryk H (2013) A robust model of pseudoelasticity in shape memory alloys. International Journal for Numerical Methods in Engineering 93(7):747–769

    Google Scholar 

  • Tušek J, Engelbrecht K, Eriksen D, Dall’Olio S, Tusek J, Pryds N (2016) A regenerative elastocaloric heat pump. Nature Energy 1:1–6

    Google Scholar 

  • VHK, ARMINES (2016) Household refrigeration technology roadmap. https://www.eup-network.de/fileadmin/user_upload/Household_Refrigeration_Review_TECHNOLOGY_ROADMAP_FINAL_20160304.pdf

Download references

Acknowledgements

This work was supported by European research Council (ERC) under Horizon 2020 research and innovation program (ERC Starting Grant No. 803669), and by the Slovenian Research Agency (P2-0210).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Boštjan Brank .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Porenta, L., Brank, B., Dujc, J., Brojan, M., Tušek, J. (2020). A Shell Finite Element Model for Superelasticity of Shape Memory Alloys. In: Altenbach, H., Chinchaladze, N., Kienzler, R., Müller, W. (eds) Analysis of Shells, Plates, and Beams. Advanced Structured Materials, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-030-47491-1_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-47491-1_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-47490-4

  • Online ISBN: 978-3-030-47491-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics