Plastic Bifurcation in the Triaxial Confining Pressure Test

[+] Author and Article Information
D. Durban

Faculty of Aerospace Engineering, Technion, Haifa 32000, Israel

P. Papanastasiou

Schlumberger Cambridge Research Ltd., High Cross, Madingley Road, Cambridge CB3 0EL England

J. Appl. Mech 67(3), 552-557 (Jan 31, 2000) (6 pages) doi:10.1115/1.1309546 History: Received March 09, 1999; Revised January 31, 2000
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.


Cheng,  S. Y., Ariaratnam,  S. T., and Dubey,  R. N., 1971, “Axisymmetric Bifurcation in an Elastic-Plastic Cylinder Under Axial Load and Lateral Hydrostatic Pressure,” Q. Appl. Math., 21, pp. 41–51.
Hutchinson,  J. W., and Miles,  J. P., 1974, “Bifurcation Analysis of the Onset of Necking in an Elastic-Platic Cylinder Under Uniaxial Tension,” J. Mech. Phys. Solids, 22, pp. 61–71.
Miles,  J. P., and Nuwayhid,  U. A., 1985, “Bifurcation in Compressible Elastic-Plastic Cylinder Under Uniaxial Tension,” Appl. Sci. Res., 42, pp. 33–54.
Drescher,  A., and Vardoulakis,  I., 1982, “Geometric Softening in Triaxial Tests on Granular Material,” Geotechnique, 32, pp. 291–303.
Vardoulakis,  I., 1983, “Rigid Granular Plasticity Model and Bifurcation in the Triaxial Test,” Acta Mech., 49, pp. 57–79.
Chau,  K.-T., 1992, “Non-Normality and Bifurcation in a Compressible Pressure-Sensitive Circular Cylinder Under Axially Symmetric Tension and Compression,” Int. J. Solids Struct., 29, pp. 801–824.
Yatomi, C., and Shibi, T., 1997, “Antisymmetric Bifurcation Analysis in a Circular Cylinder of a Non-Coaxial Cam-Clay Model,” Deformation and Progressive Failure in Geomechanics, IS-Nagoya, 1997, Pergamon, Elsevier, Oxford, UK, pp. 9–14.
Sulem,  J., and Vardoulakis,  I., 1990, “Bifurcation Analysis of the Triaxial Test on Rock Specimens: A Theoretical Model for Shape and Size Effect,” Acta Mech., 83, pp. 195–212.
Chau,  K.-T., 1993, “Antisymmetric Bifurcation in a Compressible Pressure-Sensitive Circular Cylinder Under Axisymmetric Tension and Compression,” ASME J. Appl. Mech., 60, pp. 282–289.
Chau,  K.-T., 1995, “Buckling, Barelling, and Surface Instabilities of a Finite, Transversely Isotropic Circular Cylinder,” Q. Appl. Math., 53, pp. 225–244.
Vardoulakis, I., and Sulem, J., 1995, “Bifurcation Analysis in Geomechanics,” Blackie A & P, Chapman & Hall, London.
Papanastasiou,  P., and Durban,  D., 1999, “Bifurcation of Elastoplastic Pressure Sensitive Hollow Cylinders,” ASME J. Appl. Mech., 66, pp. 117–123.
Durban,  D., and Papanastasiou,  P., 1997, “Cylindrical Cavity Expansion and Contraction in Pressure Sensitive Geomaterials,” Acta Mech., 122, pp. 99–122.
Kardomateas,  G. A., 1993, “Stability Loss in Thick Transversely Isotropic Cylindrical Shells Under Axial Compression,” ASME J. Appl. Mech., 60, pp. 506–513.
Elliot,  H. A., 1948, “Three-Dimensional Stress Distribution in Hexagonal Aelotropic Crystals,” Proc. Cambridge Philos. Soc., 44, pp. 522–533.
Papanastasiou,  P., and Durban,  D., 1997, “Elastoplastic Analysis of Cylindrical Cavity Problems in Geomaterials,” Int. J. Num. Anal. Meth. Geomech., 21, pp. 121–132.
Papamichos,  E., and Vardoulakis,  I., 1995, “Shear Band Formation in Sand According to Non-Coaxial Plasticity Model,” Geotechnique, 45, pp. 649–661.


Grahic Jump Location
Variation of characteristic roots γ23 with axial stress σ for different levels of confining pressure p. Results are for Castlegate sandstone and with deformation theory. The roots γ23 are complex conjugates from initial yield onwards up to the ellipticity limit where the equations become hyperbolic.
Grahic Jump Location
Lowest bifurcation stresses for Castlegate sandstone with zero confining pressure (p=0) under axial compression σ. Results are with deformation theory and the ellipticity limit (e.l.) is indicated by a broken line.
Grahic Jump Location
Levels of effective plastic strain εp at bifurcation. Data as in Fig. 2.
Grahic Jump Location
Bifurcation stresses. Data as in Fig. 2 but with confining pressure p=20 MPa.
Grahic Jump Location
Effective plastic strain at bifurcation. Data as in Fig. 4.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In