Skip to main content

Finite Element Method Modelling of Long and Short Hyperelastic Cylindrical Tubes

  • Conference paper
  • First Online:
XXX Russian-Polish-Slovak Seminar Theoretical Foundation of Civil Engineering (RSP 2021) (RSP 2021)

Abstract

The paper presents a study on modelling a rubber cylindrical tube in the finite element method software. It begins with a definition of stored energy functions of considered hyperelastic models. The main part of the paper concerns the problem under the plane deformation assumption, which physically may accurately approximate a sufficiently long tube. It is modelled in ABAQUS using two approaches. The first one consists of a quarter of the cross-section with boundary conditions that impose symmetry. The other FEM model involves an axially symmetric stress formulation. Results are compared with values obtained analytically. The paper ends with an example of numerical solutions for a short cylindrical tube without plane strain assumption.

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 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
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

Similar content being viewed by others

References

  1. Chadwick, P.: Thermo-Mechanics of Rubberlike Materials. Philos. Trans. Roy. Soc. Math. Phys. Eng. Sci. 276(1260), 371–403 (1974)

    MATH  Google Scholar 

  2. Zahorski, S.: A form of the elastic potential for rubber-like materials. Arch. Mater. 5, 613–618 (1959)

    MathSciNet  Google Scholar 

  3. Jemioło, S.: Studium hipersprężystych własności materiałów izotropowych, Modelowanie i implementacja numeryczna, Prace Naukowe, Budownictwo, z. 140, OWPW, Warszawa (2002)

    Google Scholar 

  4. Suchocki, C., Jemioło, S.: On finite element implementation of polyconvex incompressible hyperelasticity. Theory, Coding and Applications (2019)

    Google Scholar 

  5. Dassault Systèmes: Abaqus 2016 Theory Guide. (2015)

    Google Scholar 

  6. Anani, Y., Rahimi, G.H.: On the stability of internally pressurized thick-walled spherical and cylindrical shells made of functionally graded incompressible hyperelastic material. Latin Am. J. Solids Struct. 15(4), 1–17 (2018)

    Article  Google Scholar 

  7. Dragoni, E.: The radial compaction of hyperelastic tube as a benchmark in compressible finite elasticity. Int. J. Non-Linear Mechanics 31(4), 483–493 (1996)

    Article  Google Scholar 

  8. Han, Y., Duan, J., Wang, S.: Benchmark problems of hyper-elasticity analysis in evaluation of FEM. Materials 13(4), 885 (2020)

    Article  Google Scholar 

  9. Horgan, C.O., Saccomandi, G.: A description of arterial wall mechanics using limiting chain extensibility constitutive models. Biomech. Model. Mechanobiol. 1(4), 251–266 (2003)

    Article  Google Scholar 

  10. Ogden, R.W.: Non-Linear Elastic Deformations. Ellis Horwood, Chichester (1984)

    MATH  Google Scholar 

  11. Bonet, J., Wood, R.D.: Nonlinear Continuum Mechanics for Finite Element Analysis, 2nd edn. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  12. Alexander, H.: A constitutive relation for rubber-like materials. Int. J. Eng. Sci. 6(9), 549–563 (1968)

    Article  Google Scholar 

  13. Wolfram Research, Inc., System Modeler, Version 12.2, Champaign, IL (2020)

    Google Scholar 

  14. Taghizadeh, D.M., Bagheri, A.: Darijani, H: On the hyperelastic pressurized thick-walled spherical shells and cylindrical tubes using the analytical closed-form solutions. Int. J. Appl. Mech. 7(2), 1150027 (2015)

    Article  Google Scholar 

  15. Pamplona, D.C., Gonc-Alves, P.B., Lopes, S.R.X.: Finite deformations of cylindrical membrane under internal pressure. Int. J. Mech. Sci. 48, 683–696 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stanisław Jemioło .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jemioło, S., Franus, A. (2022). Finite Element Method Modelling of Long and Short Hyperelastic Cylindrical Tubes. In: Akimov, P., Vatin, N. (eds) XXX Russian-Polish-Slovak Seminar Theoretical Foundation of Civil Engineering (RSP 2021). RSP 2021. Lecture Notes in Civil Engineering, vol 189. Springer, Cham. https://doi.org/10.1007/978-3-030-86001-1_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-86001-1_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86000-4

  • Online ISBN: 978-3-030-86001-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics