Summary
Diffuse and localized bifurcation modes in axisymmetric, rectilinear deformations on rigid-granular dilatant material are analyzed. Rigid-granular behavior is described by a Mohr-Coulomb, single-hardening, rigid-plastic model with non-associated flow rule. Diffuse bulging in the compression test and diffuse necking in the extension test are always possible in the vicinity of the plastic limiting state. Localizations in the compression test occur in the softening regime, and in the extension test they occur in the hardening regime of the considered stress ratio-strain curve.
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Needleman, A.: Non-normality and bifurcation in plane strain tension and compression. J. Mech. Phys. Solids27, 231–254 (1979).
Vardoulakis, I.: Bifurcation analysis of the plane rectilinear deformation on dry sand samples. Int. J. Solids Structures17, 1085–1101 (1981).
Hill, R., Hutchinson, J. W.: Bifurcation phenomena in the plane tension test. J. Mech. Phys. Solids23, 239–264 (1975).
Young, N. J. B.: Bifurcation phenomena in the plane compression test. J. Mech. Phys. Solids24, 77–91 (1976).
Cheng, S. Y., Ariaratnam, S. T., Dubey, R. N.: Axisymmetric bifurcation in a elastic-plastic cylinder under axial load and lateral hydrostatic pressure. Quart. Appl. Mathematics29, 41–51 (1971).
Hutchinson, J. W., Miles, J. P.: Bifurcation analysis of the onset of necking in an elastic/plastic cylinder under uniaxial tension. J. Mech. Phys. Solids22, 61–71 (1974).
Vardoulakis, I.: Bifurcation analysis of the triaxial test on sand samples. Acta Mechanica32, 35–54 (1979).
Stören, S., Rice, J. R.: Localized necking in thin sheats. J. Mech. Phys. Solids23, 421–441 (1975).
Vardoulakis, I.: Constitutive properties of dry sand, observable in the triaxial test. Acta Mechanica38, 219–239 (1981).
Rudnicki, J. W., Rice, J. R.: Conditions for the localization of the deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids23, 371–394 (1975).
Vardoulakis, I.: Rigid granular model for sand and the influence of the deviatoric flow rule. Mech. Res. Comm.8, 275–280 (1981).
Shanley, F. R.: Inelastic column theory. I. Aeronaut. Sci.14, 261–268 (1947).
Thomas, T. Y.: Plastic flow and fracture in solids. New York: Academic Press 1961.
Truesdell, C., Noll, W.: Non-linear field theories of mechanics. (Flügge's Handbuch der Physik, III/3) Berlin-Heidelberg-New York: Springer 1965.
Vardoulakis, I.: Equilibrium bifurcation of granular earth bodies. Advances in Analysis of Geotechnical Instabilities, University of Waterloo Press, SM Study No. 13, 65–119 (1978).
Goldscheider, M.: Grenzbedingung und Fließregel von Sand. Mech. Res. Comm.3, 463–468 (1976).
Kolymbas, D.: A rate-dependent constitutive equation for soils. Mech. Res. Comm.4, 367–372 (1977).
Vardoulakis, I.: Shear band inclination and shear modulus of sand in biaxial tests. Int. J. Num. Anal. Meth. Geomech.4, 103–119 (1980).
Mehrabadi, M. M., Cowin, S. C.: Prefailure and post-failure soil plasticity models. ASCE J. Engr. Mech. Div. Proc.106, 991–1003 (1980).
Rowe, P. W.: Theoretical meaning and observed values of deformation parameters for soil. Proc. Roscoe Mem. Symp., Cambridge University (Perry, R. H. G., ed.), pp. 143–194. 1971.
Hettler, A.: Verschiebungen starrer und elastischer Gründungskörper in Sand bei monotoner und zyklischer Belastung. Dissertation, Universität Karlsruhe, 1981.
Reads, D. W., Green, G. E.: Independent stress control and triaxial extension tests on sand. Geotechnique26, 551–576 (1976).
Zimmerman, K. L., Elder, A. S., Depue, A. K.: Users manual for the BRL subroutine to calculate Bessel functions of integral order and complex argument. Tech. Report ARBRL-TR-02068, U.S. Army Armament Res. and Dev. Cmd., Ballistic Res. Lab., Aberdeen (1978).
Goldscheider, M.: Materialverhalten von Sand. Manuscript. Oberwolfach Jan. 1977.
Bishop, A. W., Green, G. E.: The influence of end restraint on the compression strength of cohensionless soil. Geotechnique23, 243–266 (1973).
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Vardoulakis, I. Rigid granular plasticity model and bifurcation in the triaxial test. Acta Mechanica 49, 57–79 (1983). https://doi.org/10.1007/BF01181755
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DOI: https://doi.org/10.1007/BF01181755