Triaxial Test Instability of a Nonassociated Flow‐Rule Model
Publication: Journal of Engineering Mechanics
Volume 119, Issue 6
Abstract
The Mohr‐Coulomb yield condition with a nonassociated flow rule is often used to model the behavior of dry or drained sand. A previous paper demonstrated, using a single shear band with a rotating orientation, that a genuine but limited instability would occur in such a model at each state of triaxial stress in the inelastic range. This paper develops the equations, explores the quantitative behavior of the model, and examines possible alternative patterns of deformation. The extent of the unstable jumps in plastic strains (0.01) and displacements, and the largely hidden transient stress jumps (15%), are calculated for such a model of sand with properties similar to those given by Lade in his papers reporting triaxial test stability in the wedge region. When the incremental elastic response is too small to stabilize the plastic, any similar model with a nonassociated flow rule likewise is unstable. The mathematical requirements for stability and the modeling of stable granular media are commented upon briefly.
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References
1.
Drucker, D. C. (1951). “A more fundamental approach to stress‐strain relations.” Proc., 1st U.S. Nat. Congr. of Appl. Mech., ASME, New York, N.Y., 487–491.
2.
Drucker, D. C. (1960). “Plasticity.” in Structural Mechanics. J. N. Goodier and N. J. Hoff, eds., Pergamon Press, New York, N.Y., 407–455.
3.
Drucker, D. C. (1964). “On the postulate of stability of material in the mechanics of continua.” Jl. de Mecanique, 3(2), Montrouge, France, 235–249.
4.
Drucker, D. C. (1988). “Conventional and unconventional plastic response and representation.” Appl. Mech. Rev., 41(4), 151–167.
5.
Drucker, D. C., Gibson, R. E., and Henkel, D. J. (1957). “Soil mechanics and work‐hardening theories of plasticity.” Trans., ASCE, 122, 338–346.
6.
Drucker, D. C., and Li, M. (1992). “Non‐associated plastic deformation and genuine instability.” Acta Mechanica, [Suppl] 3, 161–171.
7.
Drucker, D. C., and Seereeram, D. (1987). “Remaining at yield during unloading and other unconventional elastic‐plastic response.” J. Appl. Mech., 54(1), 22–26.
8.
Hashiguchi, K. (1991). “Inexpedience of the non‐associated flow rule.” Int. J. Num. Anal. Meth. Geomech., 15(10), 753–755.
9.
Hill, R. (1962). “Acceleration waves in solids.” J. Mech. Phys. Solids, 10(1), 1–16.
10.
Lade, P. V., Nelson, R. B., and Ito, Y. M. (1987). “Nonassociated flow and stability of granular materials.” J. Engrg. Mech., ASCE, 113(9), 1302–1318.
11.
Lade, P. V., and Pradel, D. (1990). “Instability and plastic flow of soils. I: Experimental observations.” J. Engrg. Mech., ASCE, 116(11), 2532–2550.
12.
Mroz, Z. (1966). “On the forms of constitutive laws for elastic‐plastic solids.” Arch. Mech. Stosowanej, 18(1), Warsaw, Poland, 1–34.
13.
Molenkamp, F., and van Ommen, A. (1987). “Peculiarity of non‐associativity in plasticity of soil mechanics.” Int. J. Num. Anal. Meth. Geomech., 11, 659–661.
14.
Needleman, A. (1979). “Non‐normality and bifurcation in plane strain tension and compression.” J. Mech. Phys. Solids, 27(3), 231–254.
15.
Pradel, D., and Lade, P. V. (1990). “Instability and plastic flow of soils. II: Analytical investigation.” J. Engrg. Mech., ASCE, 116(11), 2551–2565.
16.
Rice, J. R. (1976). “The localization of plastic deformation.” Theoretical and Applied Mechanics, W. T. Koiter, North‐Holland, Amsterdam, The Netherlands, 207–220.
17.
Rudnicki, J. W., and Rice, J. R. (1975). “Conditions for the localization of deformation in pressure‐sensitive dilatant materials.” J. Mech. Phys. Solids, 23(6), 371–394.
18.
Sandier, I. S., and Rubin, D. (1987). “The consequences of non‐associated plasticity in dynamic problems.” Constitutive laws for engineering materials: Theory and applications, C. S. Desai, Elsevier Science Publishing Co., Inc., New York, N.Y., 345–353.
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Copyright © 1993 American Society of Civil Engineers.
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Received: Aug 20, 1992
Published online: Jun 1, 1993
Published in print: Jun 1993
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