Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-18T18:46:10.942Z Has data issue: false hasContentIssue false
  • English
  • Français

The stress tensor in a two-dimensional granular shear flow

Published online by Cambridge University Press:  21 April 2006

Charles S. Campbell  and
Ailing Gong
Charles S. Campbell
Affiliation:
Department of Mechanical Engineering, University of Southern California. Los Angeles, California 90089–1453
Ailing Gong
Affiliation:
Department of Mechanical Engineering, University of Southern California. Los Angeles, California 90089–1453
Get access Rights & Permissions [Opens in a new window]

Abstract

A computer simulation is used to make a detailed study of the stress tensor in a simple shear flow of two-dimensional disks. The stresses are shown to arise from two momentum-transfer mechanisms: the 'streaming’ or kinetic mode. By which momentum is carried by particles are they move through the bulk material: and the collisional mode, by which momentum is transferred from one point to another in the material by interparticle collisions. As might be expected, the results show that the streaming mode dominates at disperse packings and the collisional mode dominates at dense packings. The friction coefficient, the ratio of shear to normal forces, is shown to decrease at high particle packing for both the collisional and streaming modes of transport. Normal-stress differences are observed within the shear plane and are evident in both the streaming and collisonal parts.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 164 , March 1986 , pp. 107 - 125
Copyright
© 1986 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ackermann, N. L. & Shen, H. 1979 Stresses in rapidly sheared fluid—solid mixtures. J. Engng Mech. Div. ASCE, 108, 95–113.Google Scholar
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid particles in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 49–63.Google Scholar
Campbell, C. S. 1982 Shear Flows of Granular Materials. Ph.D. thesis and Rep. E-200.7, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, Ca.
Campbell, C. S. & Brennen, C. E. 1985a Computer simulation of granular shear flows. J. Fluid Mech. 151, 167–188.Google Scholar
Campbell, C. S. & Brennen, C. E. 1985b Chute flows of granular material: some computer simulations. Trans. A8ME E: J. Appl. Mech. 52, 172–178Google Scholar
Carnahan, N. F. & Starling, K. E. 1969 Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635–636.Google Scholar
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases, 3rd edn. Cambridge University Press.
Cundall, P. A. 1974 A computer model for rock-mass behaviour using interactive graphics for input and output of geometrical data. US Army Corps. of Engrs (Missouri River Div.) Tech. Rep. No. MRD-2074.
Hanes, D. M. 1983 Studies on the mechanics of rapidly flowing granular-fluid materials. Ph.D. thesis, University of California, San Diego.
Hanes, D. M. & Inman, D. L. 1985 Observations of rapidly flowing granular-fluid flow. J. Fluid Mech. 150, 357–380.Google Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic particles. J. Fluid Mech. 130, 187–202.Google Scholar
Kanatani, K. 1979a A micropolar continuum theory of granular materials. Intl J. Engng Sci. 17, 419–432.Google Scholar
Kanatani, K. 1979b A continuum theory for the flow of granular materials. In Theoretical and Applied Mechanics (ed. Japan Natl Comm. for Theor. Appl. Mech.), vol. 27, pp. 571–578.
Kanatani, K. 1980 A continuum theory for the flow of granular materials (II). In Theoretical and Applied Mechanics (ed. Japan Natl Comm. for Theor. Appl. Mech.), vol. 28, pp. 485–497.
Lun, C. K. K. & Savage, S. B. 1985 A simple kinetic theory for granular flow of rough, inelastic, spherical particles. Trans. ASME E: J. Appl. Mech. (to appear).Google Scholar
Lun, C. K. K., Savage, S. B., Jeffrey, D. J. & Chepurniy, N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140, 223–256.Google Scholar
McTigue, D. F. 1978 A model for stresses in shear flows of granular material. In Proc. US—Japan Sem. on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 266–271.
Mroz, A. 1980 On hypoelasticity and plasticity approaches to constitutive modeling of the inelastic behaviour of soils. Intl J. Numer. and Anal. Meth. in Geomech. 4, 45–55.Google Scholar
Ogawa, S. 1978 Multi-temperature theory of granular materials. In Proc. US—Japan Sem. On Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 208–217.
Ogawa, S. & Oshima, N. 1977 A thermomechanical theory of soil-like materials. In Theoretical and Applied Mechanics (ed. Japan Natl Comm. for Theor. Appl. Mech.), vol. 25, pp. 229–244.
Oshima, N. 1978 Continuum model of fluidized granular media, In Proc. U.S.—Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 189–202.Google Scholar
Oshima, N. 1980 Dynamics of fluidized granular material. In Theoretical and Applied Mechanics (ed. Japan Natl Comm. for Theor. Appl. Mech.), vol. 28, pp. 475–84.
Savage, S. B. 1979 Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92, 53–96.Google Scholar
Savage, S. B. 1984 The mechanics of rapid granular flows, Advances in Applied Mechanics, vol. 24 (ed. J. Hutchinson & T. Y. Wu), pp. 289–366. Academic.
Savage, S. C. & Jeffrey, D. J. 1981 The stress tensor in a granular flow at high shear rates. J. Fluid Mech. 110, 255–272.Google Scholar
Savage, S. B. & Sayed, M. 1984 Stresses developed by dry cohesionless granular materials in an annular shear cell. J. Fluid Mech. 142, 391–430.Google Scholar
Spencer, A. J. M. 1981 Deformation of an ideal granular material. In Mechanics of Solids, Rodney Hill 60 Anniversary Volume (ed. H. G. Hopkins & J. J. Sewell), Pergamon.
Walton, O. R. 1980 Particle dynamic modelling of geological materials. Univ. of Ca. Lawrence Livermore Lab. Rep. UCRL-52915.Google Scholar
Walton, O. R. 1982a Explicit particle dynamics model for granular materials. Univ. of Ca. Lawrence Livermore Lab., Rep. UCRL-86260.Google Scholar
Walton, O. R. 1982b Particle-dynamic calculations of shear flows. Univ. of Ca. Lawrence Livermore Lab. Rep. UCRL-88560.Google Scholar