Skip to main content
SpringerLink
Log in

Buckling and barrelling instabilities in finite elasticity

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

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

References

  1. G., Aubert and R., Tahraoui: Sur la faible fermeture de certains ensembles de contraintes en elasticite non-lineaire plane.C.R. Acad. Sci., Paris 290 (1980) 537–540.

    Google Scholar 

  2. J.M., Ball: Differentiability properties of symmetric and isotropic functions.Duke Math. J. 51 (1984) 699–728.

    Google Scholar 

  3. M.F., Beatty and P., Dadras: Some experiments on the elastic stability of some highly elastic bodies.Int. J. Eng. Sci. 14 (1976) 233–238.

    Article  Google Scholar 

  4. M.F., Beatty and D.E., Hook: Some experiments on the stability of circular rubber bars under end thrust.Int. J. Solids Struct. 4 (1968) 623–635.

    Article  Google Scholar 

  5. P.J., Blatz and W.L., Ko: Application of finite elastic theory to the deformation of rubbery materials.Trans. Soc. Rheol. 6 (1962) 223–251.

    Google Scholar 

  6. P., Bridgman: The compression of sixty-one solid substances to 25,000 kg/cm2, determined by a new rapid method.Proc. Am. Acad. Arts Sci. 76 (1945) 9–24.

    Google Scholar 

  7. O., Bolza:Lectures on the Calculus of Variations. Chelsea, New York (1973).

    Google Scholar 

  8. L.W., Burgess and M., Levinson: The instability of slightly compressible rectangular rubberlike solids under biaxial loadings.Int. J. Solids Struct. 8 (1972) 133–148.

    Article  Google Scholar 

  9. R.L., Fosdick and R.T., Shield: Small bending of a circular bar superposed on finite extension or compression.Arch. Rat. Mech. Anal. 12 (1963) 223–248.

    Google Scholar 

  10. A.E., Green, R.S., Rivlin and R.T., Shield: General theory of small elastic deformations superposed on finite elastic deformations.Proc. Roy. Soc. A 211 (1952) 128–154.

    Google Scholar 

  11. R., Hill: On uniqueness and stability in the theory of finite elastic strain.J. Mech. Phys. Solids 5 (1957) 229–241.

    Article  Google Scholar 

  12. R., Hill and J.W., Hutchinson: Bifurcation phenomenon in the plane tension test.J. Mech. Phys. Solids 23 (1975) 239–264.

    Article  Google Scholar 

  13. L., Hormander:Linear Partial Differential Operators. Springer-Verlag, Berlin (1969).

    Google Scholar 

  14. L., Van Hove: Sur la signe de la variation seconde des integrales multiples a plusieurs fonctions inconnues.Mem. Acad. Roy. Belg. 24(5) (1949).

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

    Google Scholar 

  16. A.D., Kerr and S., Tang: The instability of a rectangular elastic solid.Acta. Mech. 4 (1967) 43–63.

    Google Scholar 

  17. A.D., Kerr and S., Tang: The effect of lateral hydrostatic pressure on the instability of elastic solids, particularly beams and plates.J. Appl. Mech. 33 (1966) 617–622.

    Google Scholar 

  18. J.K., Knowles and E., Sternberg: On the failure of the equations for finite elastostatic plane strain.Arch. Rat. Mech. Anal. 63 (1977) 321–336.

    Google Scholar 

  19. J.K., Knowles and E., Sternberg: On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics.J. Elast. 8 (1978) 329–379.

    Google Scholar 

  20. M., Levinson: Stability of a compressed neo-Hookean rectangular parallelepiped.J. Mech. Phys. Solids 16 (1968) 403–415.

    Article  Google Scholar 

  21. J.L., Nowinski: On the elastic stability of thick columns.Acta. Mech. 7 (1969) 279–286.

    Google Scholar 

  22. R.W. Ogden:Non-linear Elastic Deformations. Ellis-Horwood Ltd. (1984).

  23. C.E., Pearson: General theory of elastic stability.Q. Appl. Math. 14 (1956) 133–144.

    Google Scholar 

  24. R.S., Rivlin: Large elastic deformations of isotropic materials I.Phil. Trans. Roy. Soc. A 240 (1948) 459–508.

    Google Scholar 

  25. K.N., Sawyers and R.S., Rivlin: Bifurcation conditions for a thick elastic plate under thrust.Int. J. Solids Structures 10 (1974) 483–501.

    Article  Google Scholar 

  26. K.N., Sawyers and R.S., Rivlin: Stability of a thick elastic plate under thrust.J. Elast. 12 (1982) 101–125.

    Google Scholar 

  27. C.B., Sensenig: Instability of thick elastic solids.Comm. P. Appl. Math. 17 (1964) 451–491.

    Google Scholar 

  28. H.C., Simpson and S.J., Spector: On barrelling instabilities in finite elasticity.J. Elast. 14 (1984) 103–125.

    Google Scholar 

  29. H.C., Simpson and S.J., Spector: On barrelling for a special material in finite elasticity.Q. Appl. Math. 42 (1984) 99–111.

    Google Scholar 

  30. H.C. Simpson and S.J. Spector: On bifurcation in finite elasticity: buckling of a rectanglar rod. In preparation.

  31. H.C., Simpson and S.J., Spector: On the positivity of the second variation in finite elasticity.Arch. Rat. Mech. Anal. 98 (1987) 1–94.

    Google Scholar 

  32. J.L., Thompson: Some existence theorems for the traction boundary value problem of linearized elastostatics.Arch. Rat. Mech. Anal. 32 (1969) 369–399.

    Google Scholar 

  33. S.C., Wang and E.A., Meinecke: Buckling of viscoelastic columns. Part II: constant deformation rate buckling.Rubber Chem. 58 (1985) 164–175.

    Google Scholar 

  34. E.W., Wilkes: On the stability of a circular tube under end thrust.Quart. J. Mech. Appl. Math. 9 (1955) 88–100.

    Google Scholar 

  35. C.H., Wu and O., Widera: Stability of a thick rubber solid subject to pressure loads.Int. J. Solids Structures 5 (1969) 1107–1117.

    Article  Google Scholar 

  36. N.J.B., Young: Bifurcation phenomenon in the plane compression test.J. Mech. Phys. Colids 24 (1976) 77–91.

    Article  Google Scholar 

Download references

Author information

Author notes

  1. P. J. Davies

    Present address: Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada

Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Riccarton, EH 14 4AS, Edinburgh, U.K.

    P. J. Davies

Authors
  1. P. J. Davies
    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

Davies, P.J. Buckling and barrelling instabilities in finite elasticity. J Elasticity 21, 147–192 (1989). https://doi.org/10.1007/BF00040894

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00040894

Keywords

Search

Navigation