Bifurcation in elastic-plastic solids in plane stress
Authors:
R. N. Dubey and S. T. Ariaratnam
Journal:
Quart. Appl. Math. 27 (1969), 381-390
DOI:
https://doi.org/10.1090/qam/99817
MathSciNet review:
QAM99817
Full-text PDF Free Access
Abstract |
References |
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Abstract: A sufficient condition for bifurcation of equilibrium for an elastic-plastic solid under a state of plane stress is established. The bifurcation is found to occur in any of the following modes: (i) symmetric mode corresponding to necking or bulging, (ii) antisymmetric mode corresponding to buckling and (iii) mode of deformation localized at the surface.
G. R. Cowper and E. T. Onat, The initiation of necking in plane plastic flow, Proc. 4th U. S. Nat. Cong. Appl. Mech., 1023–1029 (1962)
- E. T. Onat and W. Prager, The necking of a tension specimen in plane plastic flow, J. Appl. Phys. 25 (1954), 491–493. MR 62627
- Tracy Y. Thomas, Plastic flow and fracture in solids, Mathematics in Science and Engineering, Vol. 2, Academic Press, New York-London, 1961. MR 0127630
S. T. Ariaratnam and R. N. Dubey, Some cases of bifurcation in elastic-plastic solids in plane strain, Quart. Appl. Math. 27, 349–358 (1969)
- W. Prager, Three-dimensional plastic flow under uniform stress, Rev. Fac. Sci. Univ. Istanbul (A) 19 (1954), 23–27. MR 62626
R. Hill, A general theory of uniqueness and stability in elastic-plastic solid, J. Mech. Phys. Solids, 6, 236–269 (1958)
- R. Hill, Some basic principles in the mechanics of solids without a natural time, J. Mech. Phys. Solids 7 (1959), 209–225. MR 105235, DOI https://doi.org/10.1016/0022-5096%2859%2990007-9
G. R. Cowper and E. T. Onat, The initiation of necking in plane plastic flow, Proc. 4th U. S. Nat. Cong. Appl. Mech., 1023–1029 (1962)
E. T. Onat and W. Prager, The necking of a tension specimen in plane plastic flow, J. Appl. Phys. 25, 4, 491–493 (1954)
T. Y. Thomas, Plastic flow and fracture in solids, Academic Press, New York, 1961
S. T. Ariaratnam and R. N. Dubey, Some cases of bifurcation in elastic-plastic solids in plane strain, Quart. Appl. Math. 27, 349–358 (1969)
W. Prager, Three-dimensional plastic flow under uniform stress, Rev. Fac. Sci., Istanbul Univ., 19, 1, 23–26 (1954)
R. Hill, A general theory of uniqueness and stability in elastic-plastic solid, J. Mech. Phys. Solids, 6, 236–269 (1958)
R. Hill, Some basic principles in the mechanics of solids without a natural time, J. Mech. Phys. Solids 7, 209–225 (1959)
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Article copyright:
© Copyright 1969
American Mathematical Society
