Bifurcation and Post-Bifurcation Phenomena of Elastic-Plastic Circular Tubes Subjected to External Shrinking under Plane Strain Condition

  • Y. S. Kim
  • Y. Tomita
  • A. Shindo
Conference paper


Bifurcation and post-bifurcation phenomena of thick-walled elastic-plastic circular tubes subjected to uniform shrinking are analyzed numerically under a plane strain condition. Bifurcation analysis to determine the condition for onset of bifurcation away from the axisymmetric deformation is carried out along the framework due to Hill. In order to simulate the development of shear band generating from the nonlinear growth of surface undulation over the traction-free inner surface, a finite element analysis of uniform compression of a block is performed under the plane strain condition.


Shear Band Plane Strain Condition Bifurcation Analysis Equivalent Plastic Strain Surface Undulation 
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  1. 1.
    Christoffersen, J.; Hutchinson, J.W.: A class of phenomenological corner theories of plasticity. J. Mech. Phys. Solids, 27 (1979) 465–487.MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    Needleman, A.; Tvergaard, V.: Necking of biaxially stretched elastic- plastic circular plates. J. Mech. Phys. Solids, 25 (1977) 159–183.ADSMATHCrossRefGoogle Scholar
  3. 3.
    Neale, K.W.: Phenomenological constitutive laws in finite plasticity. SM. Arch, 6 (1981) 79–128.MATHGoogle Scholar
  4. 4.
    Hill, R.: A general theory of uniqueness and stability in elastic- plastic solids. J. Mech. Phys. Solids, 6 (1958) 236–249.ADSMATHCrossRefGoogle Scholar
  5. 5.
    Hill, R.; Hutchinson, J.W.: Bifurcation phenomena in the plane strain tension test. J. Mech. Phys. Solids, 23 (1975) 239–264.MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    Tvergaard, V.: Influence of void nucleation on ductile shear fracture at a free surface. J. Mech. Phys. Solids, 30 (1982) 399–425.ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • Y. S. Kim
    • 1
  • Y. Tomita
    • 2
  • A. Shindo
    • 2
  1. 1.Graduate School of Science and TechnologyKobe UniversityNada, Kobe, 657Japan
  2. 2.Faculty of EngineeringKobe UniversityNada, Kobe, 657Japan

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