Comparison of the Rudnicki-Rice and Vermeer Bifurcation Criteria
Publication: Journal of Engineering Mechanics
Volume 143, Issue 6
Abstract
Strain localization refers to the formation of narrow zones of intense deformation in materials as a result of bifurcation in the stress-strain response during loading. Bifurcation occurs before the theoretical peak strength is reached and is then followed by strain softening. Theories and criteria have been developed to predict the point of this bifurcation in stress-strain relations. Two bifurcation criteria have been proposed for geomaterials: the complex Rudnicki-Rice criterion and the simple Vermeer criterion. The Rudnicki-Rice criterion is for strain-controlled loading, whereas the Vermeer criterion is for stress-controlled loading. This paper reviews and presents a rigorous and theoretical comparison of the two bifurcation criteria in the context of the flow theory of strain hardening elastoplasticity and shows that the simple Vermeer’s criterion is equivalent to the more complicated Rudnicki-Rice criterion for two-dimensional (2D) loading conditions. However, important differences between the two criteria exist for three-dimensional (3D) loading conditions. This paper also shows that the Rudnicki-Rice criterion provides a more realistic prediction of strain localization in geomaterials during 3D loading than does the Vermeer criterion. The paper is envisioned to offer an improved understanding of strain localization in geomaterials.
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References
Alshibli, K. A. and Sture, S. (2000). “Shear band formation in plane strain experiments of sand.” J. Geotech. Geoenviron. Eng., 495–503.
Arthur, J. R. F., Dunstan, T., Al-Ani, Q. A. J., and Assadi, A. (1977). “Plastic deformation and failure in granular materials.” Géotechnique, 27(1), 53–74.
Chambon, R. (2005). “Some theoretical results about second order work, uniqueness existence and controllability independent of the constitutive equation.” J. Eng. Math., 52(1), 53–61.
Chambon, R., Crochepeyre, S., and Desrues, J. (2000). “Localization criteria for nonlinear constitutive equations of geomaterials.” Mech. Cohes.-Frict. Mater., 5(1), 61–82.
de Borst, R. (1988). “Bifurcations in finite element models with a nonassociated flow law.” Intl. J. Numer. Anal. Methods Geomech., 12(1), 99–116.
Desrues, J. (1984). “La localisation de la déformation dans les matériaux granulaires.” Thèse de doctorat es Sciences, USMG-INPG Grenoble, France.
Guéguen, Y., and Bésuelle, P. (2007). “Damage and localization: Two key concepts in rock deformation studies.” Geol. Soc., London, Specl. Publ., 289(1), 7–17.
Gutierrez, M., and Ishihara, K. (2000). “Non-coaxiality and energy dissipation in granular materials.” Soils Found., 40(2), 49–59.
Hadamard, J. (1903). Leçons sur la Propagation des Ondes et les Équations de l’Hydrodynamique, Librairie Scientifique, A. Hermann, Sorbonne, Paris.
Han, C., and Drescher, A. (1993). “Shear bands in biaxial tests on dry coarse sand.” Soils Found., 33(1), 118–132.
Hill, R. (1962). “Acceleration waves in solids.” J. Mech. Phys. Solids, 10(1), 1–16.
Imposimato, S., and Nova, R. (1998). “An investigation on the uniqueness of the incremental response of elastoplastic models for virgin sand.” Mech. Cohes.-Frict. Mater., 3(1), 65–87.
Jenkins, J. T (1990). “Localization in granular materials.” Appl. Mech. Rev., 43(5S), S194–S195.
Lade, P. V. (2002). “Instability, shear banding, and failure in granular materials.” Intl. J. Solids Struct., 39(13–14), 3337–3357.
Lazari, M., Sanavia, L., and Schrefler, B. A. (2015). “Local and non-local elasto-viscoplasticity in strain localization analysis of multiphase geomaterials.” Intl. J. Num. Analy. Meth. Geomech., 39(14), 1570–1592.
Mandel, J. (1966). “Conditions de stabilité et postulat de Drucker.” Proc., IUTAM Symp. on Rheology Soil Mechanics, Springer, Berlin, 58–68.
Nova, R. (1985). “An engineering approach to shear band formation in geological media.” Proc., 5th Int. Conf. on Numerical Methods in Geomechanics, A.A. Balkema, Rotterdam, Netherlands, 509–616.
Nova, R. (1994). “Controllability of the incremental response of soil specimens subjected to arbitrary loading programmes.” J. Mech. Behaviour Mater., 5(2), 193–202.
Oka, F., and Kimoto, S. (2012). Computational modeling of multiphase geomaterials, CRC Press, Boca Raton, FL, 410.
Ord, A., Vardoulakis, I., and Kajewski, R. (1991). “Shear band formation in Gosford sandstone.” Int. J. Rock Mech. Mining Sci. Geomech. Abs., 28(5), 397–409.
Regueiro, R. A., and Borja, R. I. (1999). “A finite element model of localized deformation in frictional materials taking a strong discontinuity approach.” Finite Elem. Anal. Des., 33(4), 283–315.
Rice, J. R. (1976). “The localization of plastic deformation.” Proc., 14th Int. Congress on Theoretical and Applied Mechanics, W. T. Koiter, ed., NorthHolland Publishing, Amsterdam, Netherlands, 207–220.
Roscoe, K. H. (1970). “The influence of strain in soil mechanics.” Géotechnique, 20(2), 129–170.
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.
Sulem, J. (2010). “Bifurcation theory and localization phenomena.” Euro. J. Envir. Civil Eng., 14(8–9), 989–1009.
Tatsuoka, F., Nakamura, S., Huang, C. C., and Tani, K. (1990). “Strength anisotropy and shear band direction in plane strain tests of sand.” Soils Found., 30(1), 35–54.
Thomas, T. Y. (1961). Plastic flow and fracture in solids, Academic Press, New York.
Vardoulakis, I. (1980). “Shear band inclination and shear modulus of sand in biaxial tests.” Intl. J. Num. Analy. Meth. Geomech., 4(2), 155–168.
Vardoulakis, I., and Graf, B. (1985). “Calibration of constitutive models for granular materials using data from biaxial experiments.” Géotechnique, 35(3), 299–317.
Vermeer, P. A. (1982). “A simple shear-band analysis using compliances.” Proc., IUTAM Conf. on Deformation and Failure of Granular Materials, A.A. Balkema, Rotterdam, Netherlands, 493–499.
Vermeer, P. A. and de Borst, R. (1984). “Non-associated plasticity for soils, concrete and rock.” Heron, 29(3), 3–64.
Wan, R. G., Chan, D. H., and Morgenstern, N. R. (1990). “A finite element method for the analysis of shear bands in geomaterials.” Finite Elem. Anal. Des., 7(2), 129–143.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 6 • June 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Mar 3, 2016
Accepted: Nov 1, 2016
Published online: Feb 16, 2017
Published in print: Jun 1, 2017
Discussion open until: Jul 16, 2017
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