Summary
A gradient dependent dilatancy condition is assumed in order to capture the heterogeneous character of deformation in granular soils. This assumption is incorporated into the structure of classical deformation and flow theories of plasticity and its implications in two interesting examples of patterning instability, that is shear banding and liquefaction, are examined. Shear banding is considered within a modified gradient dependent deformation theory, while liquefaction is studied within a modified gradient dependent flow theory of plasticity. In both cases a deformation induced length scale is obtained near the instability, and this is identified with the thickness of the shear band or the spacing of the liquefying strips.
Übersicht
Lokale Inhomogenitäten bei der Verformung granularer Materialien sind hier mit Hilfe einer gradientenabhängigen Dilatanzbeziehung beschrieben. Diese Annahme ist in die Struktur einer klassischen Deformations- und Fließtheorie der Plastizität eingebaut, und die hiermit einhergehenden Konsequenzen werden anhand zweier interessanten Fälle der Musterbildung in Böden, nämlich Scherfugenbildung und Verflüssigung, studiert. Scherfugenbildung ist innerhalb einer modifizierten gradientenabhängigen Deformationstheorie untersucht, wogegen Bodenverflüssigung innerhalb einer modifizierten Fließtheorie analysiert wird. In beiden Fällen bekommt man in der Umgebung des Instabilitätszustandes einen deformationsinduzierten Längenmaßstab, der sich als Scherfugendicke oder als Abstand der verflüssigten Bodenstreifen manifestiert.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Rudnicki, J. W.; Rice, J. R.: Conditions for the localization of the deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Sol. 23 (1975) 371–394
Vardoulakis, I.: Shear band inclination and shear modulus of sand in biaxial tests. Int. J. Num. Anal. Meth. Geomech. 4 (1980) 103–119
Vermeer, P. A.: A simple shear band analysis using compliances. In: Vermeer, P. A. et al. (eds.) JUTAM Conf. on deformation and failure of granular materials, pp. 493–499. Rotterdam: Balkema 1982
Molenkamp, F.: Comparison of frictional material models with respect to shear band initiation. Geotechnique 35 (1985) 127–143
Rice, J. R.: On the stability of dilatant hardening for saturated rock masses. J. Geophys. Res. 80 (1975) 1531–1536
Vardoulakis, I.: Dynamic stability analysis of undrained simple shear on water-saturated granular soils. Int. J. Num. Anal. Meth. Geomech. 10 (1986) 177–190
Aifantis, E. C.: On the problem of diffusion in solids. Acta Mech. 37 (1980) 265–296
Aifantis, E. C.: On the microstructural origin of certain inelastic models. Trans. ASME J. Mat. Eng. Tech. 106 (1984) 326–330
Aifantis, E. C.: Continuum models for dislocated states and media with microstructures. In: Aifantis, E. C.; Hirth, J. P. (eds.) The mechanics of dislocations (Proc. Int. Symp. held at Houghton, Michigan, August 28–31, 1983), pp. 127–146. Metals Park: ASM 1985
Aifantis, E. C.: The physics of plastic deformation. Int. J. Plasticity 3 (1987) 211–247
Aifantis, E. C.: Application of mixture theory to fluid saturated geologic media. In: Saxena, S. K. (ed.) Compressibility phenomena in subsidence (Proc. of the Engineering Foundation Conf. held at Henniker, New Hampshire, July 29–August 3, 1984), pp. 65–78. New York: Engng. Foundation 1986
Zbib, H. M.; Aifantis, E. C.: Instabilities in metals and geomaterials. A gradient approach. In: Steele, C. R.; Bevilacqua, L. (eds) I Pan American Congress of Appl. Mech. (PACAM), pp. 532–535. Rio de Janeiro: PUC-RIO 1989
Triantafyllidis, N.; Aifantis, E. C.: A gradient approach to localization of deformation — I. Hyperelastic materials. J. Elasticity 16 (1986) 225–238
Zbib, H. M.; Aifantis, E. C.: On the localization and postlocalization behavior of plastic deformation: I. On the Initiation of shear bands; II. On the evolution and thickness of shear bands; III. On the structure and velocity of the Portevin-Le Chatelier bands. Res. Mechanica 23 (1988) 261–277, 279–292, 293–305
Mühlhaus, H. B.: Scherfugenanalyse bei granularem Material im Rahmen der Cosserat-Theorie. Ing. Arch. 56 (1986) 389–399
Mühlhaus, H.-B.; Vardoulakis, I.: The thickness of shear bands in granular materials. Geotechnique 37 (1987) 271–283
Sandler, I. S.; Wright, J. P.: Strain softening. In: Nemat-Nasser, S. et al. (eds.) Mechanics of elastic and inelastic solids 6 (Proc. workshop on theoretical foundation for large-scale computations of non-linear material behavior), pp. 285–296. Dordrecht: Martinus-Nijhoff 1984
Wu, F. J.; Freund, L. B.: Deformation trapping due to thermoplastic instability in one dimensional wave propagation. J. Mech. Phys. Sol. 32 (1984) 119–132
Aifantis, E. C.; Serrin, J. B.: The mechanical theory of fluid interfaces and Maxwell's rule. Also: Equilibrium solutions in the mechanical theory of fluid microstructures. J. Colloid Interf. Sci. 96 (1983) 517–529, 530–547
Vardoulakis, I.: Theoretical and experimental bounds for shear-band bifurcation strain in biaxial tests on dry sand. Res. Mechanica 23 (1988) 239–259
Raniecki, B.; Bruhns, O. T.: Bounds to bifurcation stresses in solids with non-associated plastic flow law of finite strain. J. Mech. Phys. Sol. 29 (1981) 153–172
Mühlhaus, H.-B.: Application of Cosserat theory in numerical solutions of limit load problems. Ing. Arch. 59 (1989) 124–137
Vardoulakis, I.: Shear-banding and liquefaction in granular materials on the basis of a Cosserat continuum theory. Ing. Arch. 59 (1989) 106–113
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vardoulakis, I., Aifantis, E.C. Gradient dependent dilatancy and its implications in shear banding and liquefaction. Ing. arch 59, 197–208 (1989). https://doi.org/10.1007/BF00532250
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00532250