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
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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.
J. M. Alexander, The effect on tensile plastic instability—a fallacious argument, J. Inst. Metals 93, 366–367 (1965)
- 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 88914, DOI https://doi.org/10.1016/0022-5096%2857%2990001-7
R Hill, A general theory of uniqueness and stability in elastic-plastic solid, J. Mech. Phys. Solids 6, 236–249 (1958)
- R. Hill, Uniqueness criteria and extremum principles in self-adjoint problems of continuum mechanics, J. Mech. Phys. Solids 10 (1962), 185–194. MR 144515, DOI https://doi.org/10.1016/0022-5096%2862%2990037-6
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)
A. D. Kerr and S. Tang, The instability of a rectangular elastic solid, Acta Mech. 4, 43–63 (1967)
- W. Prager, Three-dimensional plastic flow under uniform stress, Rev. Fac. Sci. Univ. Istanbul (A) 19 (1954), 23–27. MR 62626
H. L. Pugh, The mechanical properties and deformation characteritics of metals and alloys under pressure, First Conference on Materials, A. S. T. M., 1964
- 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, DOI https://doi.org/10.1016/0020-7225%2864%2990028-X
- 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 Russian and Polish summaries). MR 162416
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)
J. M. Alexander, The effect on tensile plastic instability—a fallacious argument, J. Inst. Metals 93, 366–367 (1965)
R. Hill, On the problem of uniqueness in the theory of a rigid-plastic solid. III, J. Mech. Phys. Solids 5, 153–161 (1957)
R Hill, A general theory of uniqueness and stability in elastic-plastic solid, J. Mech. Phys. Solids 6, 236–249 (1958)
R. Hill, Uniqueness criteria and extremum principles in self-adjoint problems of continuum mechanics, J. Mech. Phys. Solids 10, 185–249 (1962)
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)
A. D. Kerr and S. Tang, The instability of a rectangular elastic solid, Acta Mech. 4, 43–63 (1967)
W. Prager, Three-dimensional plastic flow under uniform stress, Rev. Sci. Univ. Istanbul (A) 19, 23–27 (1954)
H. L. Pugh, The mechanical properties and deformation characteritics of metals and alloys under pressure, First Conference on Materials, A. S. T. M., 1964
M. J. Sewell, Inverse rigid/plastic constitutive equations, Internat. J. Engrg. Sci. 2, 317–325 (1964)
Z. Wesolowski, The axially symmetric problem of stability loss of an elastic bar subject to tension, Arch. Mech. Stos. 15, 383–395 (1963)
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)
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Article copyright:
© Copyright 1971
American Mathematical Society
