TECHNICAL PAPERS
Mar 1, 1992

Evaluation of Plastic Bifurcation for Plane Strain versus Axisymmetry

Publication: Journal of Engineering Mechanics
Volume 118, Issue 3

Abstract

Properties of discontinuous bifurcation solutions for elastic‐plastic solids are established for conventional test conditions that are pertinent to experiments on soil, powder, and rock. Typically, such conditions are characterized as plane strain and axisymmetry. A restricted form of nonassociativity is assumed, where only the volumetric portion of the flow rule is nonassociated. Apart from this restriction, the aim is to make as general predictions as possible without resorting to a specific elastic‐plastic model. It is shown that states of plane strain are far more susceptible to bifurcations than those encountered in the conventional triaxial apparatus (which represents cylindrical stress states). Moreover, the solutions for dilatant materials will rarely bifurcate under conventional triaxial compression (CTC) test conditions, while conventional triaxial extension (CTE) test conditions fall between the two extremes of plane strain and CTC. For Drucker‐Prager criterion it is shown that bifurcation is never possible in the hardening regime for CTC. These findings are in agreement with experimentally observed behavior when it can be ensured that the stress state is sufficiently homogeneous throughout the specimen.

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References

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Hill, R. (1962). “Acceleration waves in solids.” J. Mech. and Physics of Solids, 10(1), 1–6.
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Marachi, N. D., Duncan, J. M., Chan, C. K., and Seed, H. B. (1981). “Plane‐strain testing of sand.” Lab. Shear Strength of Soil, American Soc. for Testing and Materials, 294–302.
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Ottosen, N. S., and Runesson, K. (1991). “Properties of discontinuous bifurcation solutions in elasto‐plasticity.” Int. J. Solids and Struct., 27(4), 401–421.
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Peters, J. F., Lade, P. V., and Bro, A. (1988). “Shear band formation in triaxial and plane strain tests.” Advanced triaxial testing of soil and rock, R. T. Donaghe, R. C. Chaney, and M. L. Silver, eds., American Soc. for Testing and Materials, 604–627.
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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 118Issue 3March 1992
Pages: 512 - 524

History

Published online: Mar 1, 1992
Published in print: Mar 1992

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Authors

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Dunja Peric, Student Member, ASCE
Res. Asst., Dept. of Civ., Envir., and Arch. Engrg., Univ. of Colorado, Boulder, CO 80309‐0428; on leave from Gradjevinski Institut, 41000 Zagreb, Yugoslavia
Kenneth Runesson
Assoc. Prof., Dept. of Struct. Mech., Chalmers Univ. of Tech., S‐412 96 Goteborg, Sweden
Stein Sture, Member, ASCE
Prof., Dept. of Civ., Envir., and Arch. Engrg., Univ. of Colorado, Boulder, CO 80309‐0428

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