Abstract
The slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.
Similar content being viewed by others
References
G. Gudehus and J. Tejchman. Some mechanisms of a granular mass in a silo-model tests and a numerical Cosserat approach. In O. Brüller, V. Mannel, and J. Najar, editors, Advances in Continuum Mechanics, pages 178–194. Springer, 1991.
L. S. Mohan, P. R. Nott, and K. K. Rao. Fully developed flow of coarse granular materials through a vertical channel. Chem. Engng Sci., 52: 913–933, 1997.
L. S. Mohan, P. R. Nott, and K. K. Rao. A frictional cosserat model for the flow of granular materials through a vertical channel. Acta Mech., 138: 75–96, 1999.
D. M. Mueth, F. D. Georges, S. K. Greg, J. E. Peter, S. R. Nagel, and H. M. Jaeger. Signatures of granular microstructure in dense shear flows. Cond-mat, 00034333, 2000.
H. B. Mühlhaus. Shear band analysis in granular materials by Cosserat theory. Ing. Archiv., 56: 389–399, 1986.
H. B. Mühlhaus. Application of cosserat theory in numerical solution of limit load problems. Ing. Arch., 59: 124–137, 1989.
H. B. Mühlhaus and I. Vardoulakis. The thickness of shear bands in granular materials. Geotechnique, 37: 271–283, 1987.
V. V. R. Natarajan, M. L. Hunt, and E. D. Taylor. Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow. J. Fluid Mech., 304: 1–25, 1995.
R. M. Nedderman and C. Laohakul. The thickness of shear zone of flowing granular materials. Powder Technol., 25: 91–100, 1980.
P. R. Nott, K. K. Rao, and L. S. Mohan. Document in preparation, 2000.
J. R. Prakash and K. K. Rao. Steady compressible flow of granular materials through a wedge-shaped hopper: the smooth wall radial gravity problem. Chem. Engng Sci., 43: 479–494, 1988.
K. H. Roscoe. The influence of strains in soil mechanics. 10th Rankine Lecture. Geotechnique, 20: 129–170, 1970.
J. Tejchman and G. Gudehus. Silo-music and silo-quake experiments and a numerical Cosserat approach. Powder Technol., 76: 201–212, 1993.
J. Tejchman and W. Wu. Numerical study of patterning of shear bands in a Cosserat continuum. Acta Mech., 99: 61–74, 1993.
J. Tejchman and W. Wu. Numerical study on sand and steel interfaces. Mech. Res. Comm., 21 (2): 109–119, 1994.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nott, P.R., Kesava Rao, K. & Srinivasa Mohan, L. Analysis of shear bands in slow granular flows using a frictional Cosserat model. MRS Online Proceedings Library 627, 43 (2000). https://doi.org/10.1557/PROC-627-BB4.3
Published:
DOI: https://doi.org/10.1557/PROC-627-BB4.3