Coherent vortex structures in deforming granular materials
Corresponding Author
John R. Williams
Intelligent Engineering Systems Laboratory (IESL), Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
Intelligent Engineering Systems Laboratory (IESL), Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.Search for more papers by this authorNabha Rege
Intelligent Engineering Systems Laboratory (IESL), Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
Search for more papers by this authorCorresponding Author
John R. Williams
Intelligent Engineering Systems Laboratory (IESL), Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
Intelligent Engineering Systems Laboratory (IESL), Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.Search for more papers by this authorNabha Rege
Intelligent Engineering Systems Laboratory (IESL), Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
Search for more papers by this authorAbstract
Discrete element models are used to investigate the formation of coherent structures within a deforming granular material. The numerical models predict the formation of coherent vortex-like structures, even when the boundary deformations introduce zero vorticity. We name these structures circulation cells because the particles instantaneously translate and rotate as a rigid body about a common centre. They occur for all the particle shapes and material properties tested. The size of these coherent structures range from approximately 20 to 600 particles, with the largest structures being limited by the test boundaries. Circulation cells are seen to play an important role in granular deformations including the formation of shear bands. © 1997 John Wiley & Sons, Ltd.
References
- 1 G. G. Mustoe, M. Hendriksen and H.-P. Huttelmaier, eds., Proceedings of the 1st U.S. Conference on Discrete Element Methods (DEM), Colorado School of Mines, Golden CO, 1989.
- 2 J. R. Williams and G. G. W. Mustoe, eds., Proceedings of the 2nd International Conference on Discrete Element Methods (DEM), Dept. of Civil & Environmental Engineering, Massachusetts Institute of Technology, IESL Publications, 1993.
- 3 P. A. Cundall, ‘ A computer model for simulating progressive large scale movements in block rock systems’, Symp. Intl. Society of Rock Mechanics, Nancy, France, 1971.
- 4 P. A. Cundall, ‘ Ball—a program to model granular media using the distinct element method’, Technical Report TN-LN-13, Dames and Moore, Advanced Technology Group, London, 1978.
- 5 P. A. Cundall and O. D. L. Strack, ‘A distinct element model for granular assemblies’, Geotechnique, 29, 47–65 (1979).
- 6 R. Dobry and T.-T. Ng, ‘ Discrete modeling of stress–strain behaviour of granular media at small and large strains’, G. G. Mustoe, M. Henriksen and H.-P. Huttelmaier, eds. Proceedings of the 1st U.S. Conference on Discrete Element Methods (DEM), Colorado School of Mines, Golden CO, 1989.
- 7 M. Hakuno, K. Iwashita and Y. Uchida, ‘ A dem of cliff collapse and debris flow’. Proceedings of the 1st U.S. Conference on Discrete Element Methods (DEM), G. G. Mustoe, M. Henriksen and H.-P. Huttelmaier, eds. Colorado School of Mines, Golden CO, 1989.
- 8 C. Hogue and D. Newland, ‘Efficient computer simulation of moving granular particles’, Powder Technology, 78 (1), 51–66 (1994).
- 9 I. Ishibashi, T. Agarwal and S. A. Ashraf, ‘ Anisotropic behaviors of glass spheres by a discrete element model and laboratory experiment’, Proceedings of the 1st U.S. Conference on Discrete Element Methods (DEM), G. G. Mustoe, M. Henriksen and H.-P. Huttelmaier, eds. Colorado School of Mines, Golden CO, 1989.
- 10 G. G. W. Mustoe, G. Hocking and J. R. Williams, ‘ Validation of cice discrete element code for ride-up and ice ridge/cone interaction’, Proceedings ARTIC '85, San Francisco, ASCE, New York, 1985.
- 11 R. Jullien, P. Meakin and A. Pavolovitch, ‘Three-dimensional model for particle-size segregation by shaking’, Physical Review Letters, 69, 640–643 (1992).
- 12 T.-T. Ng and X. Lin, ‘ Numerical simulations of naturally deposited granular soil with ellipsoidal elements’, Proceedings of 2nd International Conference on Discrete Element Methods (DEM), J. R. Williams and G. G. W. Mustoe, eds. Dept. of Civil, Environmental Engineering, Massachussetts Institute of Technology, pp. 557–567, IESL Publications, 1993.
- 13 T.-T. Ng and H. E. Fang, ‘ Cyclic behaviour or arrays of ellipsoids with different particle shapes’, Proceedings of joint ASME Applied Mechanics and Materials Summer Conference, Mechanics of Materials with Discontinuities and Heterogeneities Symposium, UCLA, Los Angeles, AMD-Vol. 201, p. 59–70, 1995.
- 14 J. M. Ting, M. Khwaja, L. Meachum and J. Rowell, ‘An ellipse-based discrete element model for granular materials’, Int. j. numer. anal. methods geomech., 17, 603–623 (1993).
- 15 J. M. Ting and L. Meachum, ‘ Effects of bedding plane orientation on the behavior of granular systems’, Symposium on the Mechanics of Materials with Discontinuities and Heterogeneities, ASME Joint Applied Mechanics and Materials Summer Conference, eds. A. Misra and C. s. Chang, UCLA, La, Jolla CA, pp. 43–58, 1995.
- 16 P. A. Cundall, ‘Numerical experiments on localization in frictional materials’, Ingenieur-Archiv, 59, 148–159 (1989).
- 17 G. T. Drake, ‘Structural features in granular flows’, J. Geophs. Res., 95, 8681 (1990).
- 18 S. B. Savage, ‘Streaming motions in a bed of vibrationally fluidizeddd dry granular material’, J. Fluid Mech., 194, 457 (1988).
- 19 C. Laroche, S. Douady and S. Fauve, ‘Convective flow of granular masses under vertical vibrations’, J. Phys. (Paris), 50, 699 (1989).
- 20 A. C. Hoffmann, L. P. B. M. Janssen and J. Prins, ‘Particle segregation in fluidised binary mixtures’, Chem. Eng. Sci., 48, 1583–1592 (1993).
- 21 P. K. Haff, ‘Grain flow as a fluid-mechanical phenomenon’, J. Fluid Mech., 134, 401 (1983).
- 22 J. R. Williams, ' A finite element investigation of the buckling of viscous layers, Ph.D., Thesis, University of Wales, Swansea, 1977.
- 23 J. R. Williams and N. Rege, ‘Circulation cells in a deforming granular material’, Powder Technology, 90, 187–194 (1996).
- 24 J. R. Williams and N. Rege, ‘ A simulation system for computational materials’, Technical report, IESL 95–01, Dept. of Civil & Environmental Engineering, Massachusetts Institute of Technology, 1995.
- 25 The Mathworks Inc., MATLAB Reference Guide, The Mathworks Inc., Natice, MA, 1992.
- 26 K. Karhunen, ‘Aur spektral theorie stochastischer prozess’, Ann. Acad. Sci. Fennicae Ser., A1, 34 (1946).
- 27 P. Holmes, G. Berkooz and J. L. Lumley, ‘The proper orthogonal decomposition in the analysis of turbulent flows’, Annual Rev. Fluid Mech., 25, 539 (1993).
- 28 A. Elvin, ‘Number of grains required to homogenize elastic properties of polycrystalline ice’, Mechanics of Materials, 22, 51–64 (1996).
