Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Axisymmetric bifurcation in an elastic-plastic cylinder under axial load and lateral hydrostatic pressure

Authors: S. Y. Cheng, S. T. Ariaratnam and R. N. Dubey
Journal: Quart. Appl. Math. 29 (1971), 41-51
DOI: https://doi.org/10.1090/qam/99765
MathSciNet review: QAM99765
Full-text PDF

Abstract | References | Additional Information

Abstract: Conditions for initiation of necking and bulging of elastic and elastic-plastic cylindrical solids are derived. The possibility of bifurcation of rigid-plastic solids and the conditions for homogeneous deformation with homogeneous stress are also investigated.

References [Enhancements On Off] (What's this?)

  • [1] J. M. Alexander, The effect on tensile plastic instability--a fallacious argument, J. Inst. Metals 93, 366-367 (1965)
  • [2] R. Hill, On the problem of uniqueness in the theory of a rigid-plastic solid. III, J. Mech. Phys. Solids 5 (1957), 153–161. MR 0088914, https://doi.org/10.1016/0022-5096(57)90001-7
  • [3] R Hill, A general theory of uniqueness and stability in elastic-plastic solid, J. Mech. Phys. Solids 6, 236-249 (1958)
  • [4] R. Hill, Uniqueness criteria and extremum principles in self-adjoint problems of continuum mechanics, J. Mech. Phys. Solids 10 (1962), 185–194. MR 0144515, https://doi.org/10.1016/0022-5096(62)90037-6
  • [5] 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, 617-622 (1966)
  • [6] A. D. Kerr and S. Tang, The instability of a rectangular elastic solid, Acta Mech. 4, 43-63 (1967)
  • [7] W. Prager, Three-dimensional plastic flow under uniform stress, Rev. Fac. Sci. Univ. Istanbul (A) 19 (1954), 23–27. MR 0062626
  • [8] H. L. Pugh, The mechanical properties and deformation characteritics of metals and alloys under pressure, First Conference on Materials, A. S. T. M., 1964
  • [9] M. J. Sewell, Inverse rigid/plastic constitutive equations, Internat. J. Engrg. Sci. 2 (1964), 317–325 (English, with French, German, Italian, and Russian summaries). MR 0167055, https://doi.org/10.1016/0020-7225(64)90028-X
  • [10] Zbigniew Wesołowski, The axially symmetric problem of stability loss of an elastic bar subject to tension, Arch. Mech. Stos. 15 (1963), 383–395 (English, with Polish and Russian summaries). MR 0162416
  • [11] C. H. Wu and O. E. Widera, Stability of a thick rubber solid subjected to pressure loads, Int. J. Solids Structures 5, 1107-1117 (1969)

Additional Information

DOI: https://doi.org/10.1090/qam/99765
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society