Abstract
Granular material is characterized by the appearance of localization phenomena, as for instance the formation of shear bands under the influence of gravity. By means of a micromechanically motivated discrete element method (DEM), two-dimensional simulations of monodisperse circular disks are performed, where both translational and rotational degrees of freedom of the particles are taken into account by the consideration of Newtonian equations of motion for the translations and by Eulerian equations of motion for the rotations of the single particles. It turns out that even for the simplest contact laws, e. g. a combination of Coulomb and Newton type friction for the tangential contact of monodisperse particles and a repulsive damped spring normal contact force, shear bands are obtained. In the regime of small relative tangential velocities, the viscous part of the frictional contact law becomes effective. Then, “slow” relative tangential velocities are surpressed corresponding to an enforcing of rolling modes characterized by zero relative tangential velocities in the contact points and leading to an instability that corresponds to shear banding. The DEM simulations furthermore suggest that the size distribution of the assembly modifies the shape of the shear band but is not necessary for its formation. These propositions seem to be in agreement with the experimental observations reported in the paper by Viggiani et al. [23] included in this volume.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Becker and H. Lippmann: Plane plastic flow of granular model material. Arch. Mech. 29, 829–846 (1977).
R. de Boer: Vektor-und Tensorrechnung für Ingenieure. Springer-Verlag, Berlin 1982.
R. de Boer and W. Ehlers: Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme, Teil I. Forschungsberichte aus dem Fachbereich Bauwesen 40, Universität-GH-Essen 1986.
R. M. Bowen: Theory of mixtures. In A. C. Eringen (ed.), Continuum Physics, Vol. III, pp. 1–127, Academic Press, New York 1976.
R. M. Bowen: Incompressible porous media models by use of the theory of mixtures. Int. J. Engng. Sci. 20, 1129–1148 (1980).
E. Cosserat and F. Cosserat: Théorie de Corps Déformable. A. Hermann et fils, Paris 1909.
P. A. Cundall and O. D. L. Strack: A discrete numerical model for granular assemblies. Géotechnique 29, 47–65 (1979).
S. Diebels: Constitutive modelling of micropolar porous media. In J.-F. Thimus et. al. (eds.), Poromechanics-A Tribute to Maurice A. Biot, pp. 71–76. A. A. Balkema, Rotterdam 1998.
S. Diebels: A macroscopic description of the quasi-static behavior of granular materials based on the Theory of Porous Media. Granular Matter 2, 143–152 (2000).
W. Ehlers: Poröse Medien-ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Forschungsberichte aus dem Fachbereich Bauwesen 47, Universität-GH-Essen 1989.
W. Ehlers: Constitutive equations for granular materials in geomechanical context. In K. Hutter (ed.), Continuum Mechanics in Environmental Sciences and Geophysics, CISM Courses and Lectures No. 337, pp. 313–402, Springer-Verlag, Wien 1993.
W. Ehlers and W. Volk: On shear band localization phenomena of liquid-saturated granular elasto-plastic porous solids accounting for fluid viscosity and micropolar solid rotations. Mech. Cohesive-frictional Mater. 2, 301–320 (1997).
W. Ehlers and W. Volk: On shear band localization phenomena induced by elastoplastic consolidation of fluid-saturated soils. In D. R. J. Owen, E. Oñate and E. Hinton (eds.), Computational Plasticity-Fundamentals and Applications, pp. 1656–1664, CIMNE, Barcelona 1997.
W. Ehlers and W. Volk: On theoretical and numerical methods in the theory of porous media based on polar and non-polar solid materials. Int. J. Solids Structures 35, 4597–4616 (1998).
A. C. Eringen and C. B. Kafadar: Polar field theories. In A. C. Eringen (ed.), Continuum Physics, Vol. IV, Academic Press, pp. 1–73, New York 1976.
H. Haken and A. Wunderlin: Die Selbststrukturierung der Materie. Vieweg, Wiesbaden 1991.
M. Lätzel, S. Luding, and H. J. Herrmann. Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell. Granular Matter, 2(3):123–135, 2000. cond-mat/0003180.
T. Marcher and P. A. Vermeer: Macromodelling of softening in non-cohesive soils. This issue, pp. 89–110.
P. Rossi: Kinematische Modelluntersuchung von ebenen Grundbauproblemen. Diplomarbeit, Institut für Geotechnik, Universität Stuttgart 1983.
K. von Terzaghi and R. Jelinek: Theoretische Bodenmechanik. Springer-Verlag, Berlin 1954.
C. Thornton: Numerical simulations of deviatoric shear deformation of granular media. Géotechique 50, 43–53 (2000).
C. Thornton and S. J. Antony: Quasi shear deformation of a soft particle system. Powder Technology 109, 179–191 (2000).
G. Viggiani, M. Küntz and J. Desrues: Does shear banding in sand depend on grain size distribution? This issue, pp. 111–127.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ehlers, W., Diebels, S., Michelitsch, T. (2001). Microscopic modelling of granular materials taking into account particle rotations. In: Vermeer, P.A., Herrmann, H.J., Luding, S., Ehlers, W., Diebels, S., Ramm, E. (eds) Continuous and Discontinuous Modelling of Cohesive-Frictional Materials. Lecture Notes in Physics, vol 568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44424-6_18
Download citation
DOI: https://doi.org/10.1007/3-540-44424-6_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41525-1
Online ISBN: 978-3-540-44424-4
eBook Packages: Springer Book Archive