Skip to main content
Log in

Azimuthal Shear in Compressible Finite Elasticity

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

In an earlier paper, the broadest classes of compressible isotropic strain energies that support irrotational universal deformations were identified and the problems of cylindrical and spherical inflation or compaction were solved in closed form for all of these strain energies. Similar closed form solutions of the problem of azimuthal shear are presented here.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Collected Papers of R.S. Rivlin: Barenblatt, G.I., Joseph, D.D. (eds.), vol. 2. Springer, New York (1997)

  2. Truesdell, C.A., Noll, W.: The nonlinear field theories of mechanics. In: Flügge, S. (ed.) Handbuch der Physik III/3. Springer (1965)

  3. Ogden, R.W.: Non-linear elastic deformations. Ellis Horwood, Chichester (1984)

    Google Scholar 

  4. Ericksen, J.L.: Deformations possible in every compressible, isotropic, perfectly elastic material. J. Math. Phys. 34, 126–128 (1955)

    MathSciNet  Google Scholar 

  5. John, F.: Plain strain problems for a perfectly elastic material of harmonic type. Comm. Pure Appl. Math. 13, 239–296 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  6. Jafari, A.H., Abeyaratne, R., Horgan, C.O.: The finite deformation of a pressurized circular tube for a class of compressible materials. Z. Angew. Math. Phys. 35, 227–246 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  7. Abeyaratne, R., Horgan, C.O.: The pressurized hollow sphere problem in finite elastostatics for a class of compressible materials. Int. J. Solids Struct. 20, 715–723 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ogden, R.W., Isherwood, D.A.: Solution of some finite plane strain problems for compressible elastic solids. Q. J. Mech. Appl. Math. 31, 219–249 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  9. Carroll, M.M.: Finite strain solutions in compressible finite elasticity. J. Elasticity. 20, 65–92 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  10. Carroll, M.M.: Controllable deformations in compressible finite elasticity. Stab. Appl. Anal. Contin. Media 1, 373–384 (1991)

    Google Scholar 

  11. Murphy, J.G.: A family of solutions describing plane strain cylindrical inflation in finite, compressible elasticity. J. Elasticity. 45, 1–11 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Murphy, J.G.: A family of solutions describing spherical inflation in finite, compressible elasticity. Q. J. Mech. Appl. Math. 50, 35–45 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Carroll, M.M., Rooney, F.J.: Implications of Shield’s inverse deformation theorem for compressible finite elasticity. Z. Angew. Math. Phys. 56, 1048–1060 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Carroll, M.M.: Compressible isotropic strain energies that support universal irrotational finite deformations. Q. J. Mech. Appl. Math. 58, 601–614 (2005)

    Article  MATH  Google Scholar 

  15. Murphy, J.G., Carroll, M.M.: Azimuthal shearing of special compressible materials. Proc. Royal Irish Acad. 93A, 209–230 (1993)

    MathSciNet  Google Scholar 

  16. Polignone, D.A., Horgan, C.O.: Pure azimuthal shear of compressible nonlinearly elastic materials. Quart. Appl. Math. 50, 323–341 (1992)

    MATH  MathSciNet  Google Scholar 

  17. Haughton, D.M.: Circular shearing of compressible elastic cylinders. Q. J. Mech. Appl. Math. 46, 471–486 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  18. Beatty, M.F., Jiang, Q.: On compressible materials capable of sustaining axi-symmetric shear deformations. Part 2: Rotational. Q. J. Mech. Appl. Math. 50, 211–237 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. Jiang, X., Ogden, R.W.: On azimuthal shear of a circular cylindrical tube of compressible elastic material. Q. J. Mech. Appl. Math. 51, 143–158 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  20. Paullet, J.E., Warne, D.P., Warne, P.G.: Existence and Uniqueness of azimuthal shear solutions in compressible isotropic nonlinear elasticity. Math. Mech. Solids 3, 53–69 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  21. Carroll, M.M.: Irrotational finite elastic deformations. J. Appl. Mech. Trans. ASME, in press (2007)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. M. Carroll.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carroll, M.M. Azimuthal Shear in Compressible Finite Elasticity. J Elasticity 88, 141–149 (2007). https://doi.org/10.1007/s10659-007-9123-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10659-007-9123-3

Keywords

Mathematics Subject Classification (2000)

Navigation