Skip to main content
SpringerLink
Log in

On a class of exact solutions in nonlinear elasticity

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

A class of exact solutions to the equations of nonlinear elasticity that occur at constant pressure on the boundary of the body and null Cauchy deviatoric stress is presented. Stability analysis shows that the solutions in this class are at best neutrally stable.

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

Similar content being viewed by others

References

  1. E. Varley and A. Day, Equilibrium phases of elastic materials at uniform temperature and pressure.Arch. Rational Mech. Anal. 22 (1966) 253–269.

    Google Scholar 

  2. J.L. Ericksen, Kirchhoff and Gibbs revisited.J. Elasticity 8 (1978) 439–446.

    Google Scholar 

  3. J.L. Ericksen, On the symmetry and stability of thermoelastic solids.J. Appl. Mech. 45 (1978) 740–744.

    Google Scholar 

  4. S.A. Adeleke, Stability of some states of plane deformation.Arch. Rational Mech. Anal. 72 (1980) 243–263.

    Google Scholar 

  5. C. Truesdell and W. Noll, The non-linear field theories of mechanics,Handbuch der Physik Volume III/3. Berlin/Heidelberg/New York: Springer (1965).

    Google Scholar 

  6. M.F. Beatty, Stability of hyperelastic bodies subject to hydrostatic loading.Int. J. Non-Linear Mechanics 5 (1970) 367–383.

    Google Scholar 

  7. R.S. Rivlin, Some restrictions on constitutive inequalities. In: J.J. Delgado Domingos, M.N.R. Nina and J.H. Whitelaw (eds),Proc. Int. Symp. on the Foundations of Continuum Thermodynamics. London: MacMillan (1974) pp. 229–249.

    Google Scholar 

  8. R. Sidoroff, Sur les restrictions a imposer a l'energie de deformation d'un material hyperelastique.C.R. Acad. Sc. Paris 279 (1974) 379–382.

    Google Scholar 

  9. J.M. Ball, Constitutive inequalities and existence theorems in elasticity. In: R.J. Knops (ed.),Non-Linear Analysis and Mechanics: Heriot-Watt Symposium Volume I. London: Pitman (1977) pp. 187–241.

    Google Scholar 

  10. C. Truesdell and R. Toupin, The classical field theories,Handbuch der Physik Volume III/1. Berlin/Heidelberg/New York: Springer (1960).

    Google Scholar 

  11. C-C. Wang and C. Truesdell,Introduction to Rational Elasticity. Groningen: Noordhoff (1973).

    Google Scholar 

  12. A.W. Marris, Universal deformations in incompressible isotropic elastic materials.J. Elasticity 5 (1975) 111–128.

    Google Scholar 

  13. M. Aron and C. Fetecau, Some finite deformations of transversely isotropic elastic materials.Arch. Mech. 25 (1973) 377–382.

    Google Scholar 

  14. S.S. Antman, Ordinary differential equations of non-linear elasticity II: Existence and regularity for conservative boundary-value problems.Arch. Rational Mech. Anal. 61 (1976) 353–393.

    Google Scholar 

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

    Google Scholar 

  16. A. Hanyga,Mathematical Theory of Non-linear Elasticity. Chichester: Ellis Horwood (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics & Statistics, Plymouth Polytechnic, Drake Circus, PL4 8AA, Plymouth, Devon, U.K.

    M. Aron & C. F. M. Creasy

Authors
  1. M. Aron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. F. M. Creasy
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aron, M., Creasy, C.F.M. On a class of exact solutions in nonlinear elasticity. J Elasticity 21, 27–41 (1989). https://doi.org/10.1007/BF00040932

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00040932

Keywords

Search

Navigation