Skip to main content
SpringerLink
Log in

Stress analysis of a thick-walled cylinder composed of incompressible hyperelastic materials subjected to internal and/or external pressure: analytical and finite element analysis

  • Original Paper
  • Published:
Journal of Rubber Research Aims and scope Submit manuscript

Abstract

In this work, the mechanical behaviour of a thick-walled cylindrical pressure vessel composed of an incompressible isotropic non-linearly hyper-elastic material subjected to internal and/or external pressure is investigated. An analytical solution is proposed for the general form of the free strain energy density and different models including Neo–Hookean, Mooney–Rivlin, and Yeoh are employed. An analysis was conducted to determine the extension ratio at the inner and outer radii as well as the stress distribution, in different cases, namely the application of internal pressure only, external pressure only, and internal and external pressure applied simultaneously. In addition, various pressure values are applied to account for different levels of deformation. In order to strengthen the analytical solution, a finite element model of the pressurised vessel was constructed. A very good agreement has been found between the analytical predictions and the numerical results, suggesting the accuracy of the analytical solution. The analytical solution can be used for parametric studies (material or geometrical parameters) and the design/optimisation of a thick-walled cylindrical pressure vessel subjected to internal and/or external pressure. Additionally, it obviates the requirement for many finite element simulations, where computational cost is an important parameter.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Freakley PK, Payne AR, Davey A (1978) Theory and practice of engineering with rubber. Applied Science Publishers, Basel

    Google Scholar 

  2. Gent AN (2012) Engineering with rubber: how to design rubber components. Carl Hanser Verlag GmbH Co KG, Munich. https://doi.org/10.3139/9783446428713

    Book  Google Scholar 

  3. Beatty MF (1987) Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues—with examples. Appl Mech Rev. https://doi.org/10.1115/1.3149545

    Article  Google Scholar 

  4. Methia M, Bechir H, Frachon A, Aït Hocine N (2020) An asymptotic finite plane deformation analysis of the elastostatic fields at a crack tip in the framework of hyperelastic, isotropic, and nearly incompressible Neo–Hookean materials under mode-I loading. Acta Mech 231(3):929–946. https://doi.org/10.1007/s00707-019-02577-7

    Article  Google Scholar 

  5. Saccomandi G, Ogden RW (2003) Mechanics and thermomechanics of rubberlike solids. Springer, Berlin. https://doi.org/10.1007/978-3-7091-2540-3

    Book  Google Scholar 

  6. Ogden RW (1997) Non-linear elastic deformations. Courier Corporation, Chennai

    Google Scholar 

  7. Holzapfel GA (2000) Nonlinear solid mechanics a continuum approach for engineering, 1st edn. Wiley, Chichester

    Google Scholar 

  8. Marckmann G, Verron E (2006) Comparison of hyperelastic models for rubber-like materials. Rubber Chem Technol 79(5):835–858. https://doi.org/10.5254/1.3547969

    Article  CAS  Google Scholar 

  9. Steinmann P, Hossain M, Possart G (2012) Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data. Arch Appl Mech 82(9):1183–1217. https://doi.org/10.1007/s00419-012-0610-z

    Article  Google Scholar 

  10. Hill JM (1973) Partial solutions of finite elasticity—plane deformations. Z fur Angew Math Phys 24(3):401–408. https://doi.org/10.1007/BF01595205

    Article  Google Scholar 

  11. Chadwick P, Haddon E (1972) Inflation-extension and eversion of a tube of incompressible isotropic elastic material. IMA J Appl Math 10(2):258–278. https://doi.org/10.1093/imamat/10.2.258

    Article  Google Scholar 

  12. Carroll M (1968) Finite deformations of incompressible simple solids I. Isotropic solids. Q J Mech Appl Math 21(2):147–170. https://doi.org/10.1093/qjmam/21.2.147

    Article  Google Scholar 

  13. Carroll M (1987) Pressure maximum behavior in inflation of incompressible elastic hollow spheres and cylinders. Q Appl Math 45(1):141–154. https://doi.org/10.1090/qam/885176

    Article  Google Scholar 

  14. Ericksen JL (1954) Deformations possible in every isotropic, incompressible, perfectly elastic body. Z Fur Angew Math Phys 5(6):466–489. https://doi.org/10.1007/BF01601214

    Article  Google Scholar 

  15. Ericksen J (1955) Inversion of a perfectly elastic spherical shell. ZAMM J Appl Math Mech 35(9–10):382–385. https://doi.org/10.1002/zamm.19550350909

    Article  Google Scholar 

  16. Green AE, Adkins JE (1960) Large elastic deformations and non-linear continuum mechanics. (No Title)

  17. Green AE, Zerna W (1992) Theoretical elasticity. Courier Corporation, Chennai

    Google Scholar 

  18. Rivlin RS, Barenblatt GI (1997) Collected papers of RS Rivlin. Springer Science & Business Media, Berlin

    Google Scholar 

  19. Alexander H (1971) The tensile instability of an inflated cylindrical membrane as affected by an axial load. In J Mech Sci 13(2):87–95. https://doi.org/10.1016/0020-7403(71)90013-0

    Article  Google Scholar 

  20. Amar MB, Goriely A (2005) Growth and instability in elastic tissues. J Mech Phys 53(10):2284–2319. https://doi.org/10.1016/j.jmps.2005.04.008

    Article  CAS  Google Scholar 

  21. Dorfmann A, Haughton D (2006) Stability and bifurcation of compressed elastic cylindrical tubes. Int J Eng Sci 44(18–19):1353–1365. https://doi.org/10.1016/j.ijengsci.2006.06.014

    Article  Google Scholar 

  22. Goriely A, Destrade M, Ben Amar M (2006) Instabilities in elastomers and in soft tissues. Q J Mech Appl Math 59(4):615–630. https://doi.org/10.1093/qjmam/hbl017

    Article  Google Scholar 

  23. Corneliussen AH, Shield R (1961) Finite deformation of elastic membranes with application to the stability of an inflated and extended tube. Arch Ration Mech Anal 7(1):273–304. https://doi.org/10.1007/BF00250766

    Article  Google Scholar 

  24. Haughton D, Ogden R (1979) Bifurcation of inflated circular cylinders of elastic material under axial loading—I. Membrane theory for thin-walled tubes. J Mech Phys 27(3):179–212. https://doi.org/10.1016/0022-5096(79)90001-2

    Article  Google Scholar 

  25. Chen Y (1995) Stability and bifurcation of inflated cylindrical elastic membranes. Appl Mech Mater 1:404–409

    Google Scholar 

  26. Kyriakides S, Yu-Chung C (1990) On the inflation of a long elastic tube in the presence of axial load. Int J Solids Struct 26(9–10):975–991. https://doi.org/10.1016/0020-7683(90)90012-K

    Article  Google Scholar 

  27. Kyriakides S, Yu-Chung C (1991) The initiation and propagation of a localized instability in an inflated elastic tube. Int J Solids Struct 27(9):1085–1111. https://doi.org/10.1016/0020-7683(91)90113-T

    Article  Google Scholar 

  28. Tang D, Yang C, Huang Y, Ku DN (1999) Wall stress and strain analysis using a three-dimensional thick-wall model with fluid–structure interactions for blood flow in carotid arteries with stenoses. Comput Struct 72(1–3):341–356. https://doi.org/10.1016/S0045-7949(99)00009-7

    Article  Google Scholar 

  29. Haussy B, Ganghoffer J (2002) An orthotropic hyperelastic model of cylindrical thick shells under pressure: application to the modeling of aneurysm. In: 15th American Society of Civil Engineers, engineering mechanics conference, Columbia University, New York, NY, USA, 2–5 June 2002

  30. Gonçalves PB, Pamplona D, Lopes SRX (2008) Finite deformations of an initially stressed cylindrical shell under internal pressure. In J Mech Sci 50(1):92–103. https://doi.org/10.1016/j.ijmecsci.2007.05.001

    Article  Google Scholar 

  31. Taghizadeh D, Bagheri A, Darijani H (2015) On the hyperelastic pressurized thick-walled spherical shells and cylindrical tubes using the analytical closed-form solutions. In J Appl Mech 7(2):1550027. https://doi.org/10.1142/S1758825115500271

    Article  Google Scholar 

  32. Bagheri A, Taghizadeh D, Darijani H (2016) On the behavior of rotating thick-walled cylinders made of hyperelastic materials. Meccanica 51(3):673–692. https://doi.org/10.1007/s11012-015-0233-x

    Article  Google Scholar 

  33. Zhu Y, Luo X, Ogden RW (2008) Asymmetric bifurcations of thick-walled circular cylindrical elastic tubes under axial loading and external pressure. Int J Solids Struct 45(11–12):3410–3429. https://doi.org/10.1016/j.ijsolstr.2008.02.005

    Article  Google Scholar 

  34. Shojaeifard M, Wang K, Baghani M (2020) Large deformation of hyperelastic thick-walled vessels under combined extension-torsion-pressure: analytical solution and FEM. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2020.1826963

    Article  Google Scholar 

  35. Almasi A, Baghani M, Moallemi A (2017) Thermomechanical analysis of hyperelastic thick-walled cylindrical pressure vessels, analytical solutions and FEM. Int J Mech Sci 130:426–436. https://doi.org/10.1016/j.ijmecsci.2017.06.033

    Article  Google Scholar 

  36. Benslimane A (2022) Nonlinear stress analysis of rubber-like thick-walled sphere using different constitutive models. Mater Today Proc 53:46–51. https://doi.org/10.1016/j.matpr.2021.12.284

    Article  Google Scholar 

  37. Benslimane A, Methia M, Khadimallah MA (2022) Nonlinear stress analysis of rubber-like thick-walled cylinder. J Rubber Res 25(4):345–356. https://doi.org/10.1007/s42464-022-00180-5

    Article  Google Scholar 

  38. Treloar L (1944) Stress-strain data for vulcanized rubber under various types of deformation. Rubber Chem Technol 17(4):813–825. https://doi.org/10.5254/1.3546701

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mécanique, Matériaux et Energétique (L2ME), Faculté de Technologie, Université de Bejaia, 06000, Bejaïa, Algeria

    Mounir Methia, Safia Bouzidi & Abdelhakim Benslimane

  2. LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie, Université de Tunis El Manar, École Nationale d’Ingénieurs de Tunis, 1002, Tunis, Tunisia

    Makrem Arfaoui

  3. INSA CVL, Univ. Tours, Univ. Orléans, LaMé, 3 rue de la Chocolaterie, BP 3410, 41034, Blois Cedex, France

    Nourredine Aït Hocine

Authors
  1. Mounir Methia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Safia Bouzidi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdelhakim Benslimane
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Makrem Arfaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nourredine Aït Hocine
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdelhakim Benslimane.

Ethics declarations

Conflict of interest

No potential conflict of interest was reported by the author(s).

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Methia, M., Bouzidi, S., Benslimane, A. et al. Stress analysis of a thick-walled cylinder composed of incompressible hyperelastic materials subjected to internal and/or external pressure: analytical and finite element analysis. J Rubber Res 27, 115–126 (2024). https://doi.org/10.1007/s42464-024-00239-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42464-024-00239-5

Keywords

Search

Navigation