TECHNICAL PAPERS
Aug 1, 1983

Piecewise Linear Yield Criteria in Invariant Form

Publication: Journal of Engineering Mechanics
Volume 109, Issue 4

Abstract

General piecewise‐linear yield criteria exhibiting 30°, 60°, or 120° symmetry in the octahedral plane are expressed in terms of the canonical invariants of the deviator stress, J2 and J3. Criteria of the type often associated with granular media, in which strength is proportional to the hydrostatic component of stress, are also reviewed. In the particular case of the Coulomb criterion, it is shown that compact expressions can be found through the use of the canonical invariants of stress I1, I2, and I3.

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References

1.
Haythornthwaite, R. M., “An Interpolation Scheme for Plastic Yield Criteria,” Journal of Applied Mechanics, ASME, Vol. 46, 1979, pp. 701–702.
2.
Haythornthwaite, R. M., “Mechanics of the Triaxial Test for Soils,” Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 86, No. SM5, Proc. Paper 2625, Oct., 1960, pp. 35–62.
3.
Haythornthwaite, R. M., “Range of Yield Condition in Ideal Plasticity,” Transactions, ASCE, Vol. 127, Paper 3377, Part I, 1962, pp. 1252–1268.
4.
Ivlev, D. D., “On the Development of a Theory of Ideal Plasticity,” Prikladnaia Matematika i Mekhanika, Academy of Sciences, U.S.S.R. Vol. 22, No. 6, 1958, pp. 850–855
(English translation, Pergamon Press, Inc., New York, N.Y., pp. 1221–1231).
5.
Mendelson, A., Plasticity: Theory and Application, The Macmillan Co., New York, N.Y., 1968.
6.
Prager, W., and Hodge, P. G., Jr., Theory of Perfectly Plastic Solids, John Wiley and Sons, Inc., New York, N.Y., 1951.
7.
Salencon, J., Applications of the Theory of Plasticity in Soil Mechanics, John Wiley and Sons, Inc., New York, N.Y., 1977.
8.
Shield, R. T., “On Coulomb's Law of Failure in Soils,” Journal of the Mechanics and Physics of Solids, Vol. 4, No. 1, Oct., 1955, pp. 10–16.
9.
Terzaghi, K., Theoretical Soil Mechanics, John Wiley and Sons, Inc., New York, N.Y., 1943.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 109Issue 4August 1983
Pages: 1016 - 1022

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Published online: Aug 1, 1983
Published in print: Aug 1983

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Robert M. Haythornthwaite, F. ASCE
Prof. of Engrg. Sci., Temple Univ., Philadelphia, Pa.

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