Discrete element simulations of dense packings and heaps made of spherical and non-spherical particles

Powder Technology

Volumn 109, Issue 1-3, 2000, Pages 278-292

  Matuttis, H G ^a   Luding, S ^a   Herrmann, H J ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

DEM; Friction; Non spherical particles; Numerical modeling; Sandpiles

Indexed keywords

COMPUTER SIMULATION; FINITE DIFFERENCE METHOD; FRICTION; GRAIN SIZE AND SHAPE; MATHEMATICAL MODELS; PARTICLES (PARTICULATE MATTER); SURFACE ROUGHNESS;

NONSPHERICAL PARTICLES; SANDPILES;

GRANULAR MATERIALS;

GRANULAR MEDIUM; MATHEMATICAL MODELING; PACKING; SPHERE;

ARTICLE; FLOW; FORCE; FRICTION; MECHANICS; PHENOMENOLOGY; STRESS;

EID: 0034599488     PISSN: 00325910     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0032-5910(99)00243-0     Document Type: Article

References (90)

1. Cooke M.H., Stephens D.J., Bridgewater J. Powder mixing-a literature survey. Powder Technol. 15:1976;1.
2. Campbell C.S. Rapid granular flows. Annu. Rev. Fluid Mech. 22:1990;57.
3. Geldart D., Rhodes M.J. Survey of current world-wide research in gas fluidization (Jan. 1989-Dec. 1991). Powder Technol. 71:1992;1.
4. Jaeger H.M., Nagel S.R. Physics of the granular state. Science. 255:1992;1523.
5. Jaeger H.M., Nagel S.R., Behringer R.P. The physics of granular materials. Phys. Today. 49(4):1996;32-38.
6. Jaeger H.M., Nagel S.R., Behringer R.P. Granular solids, liquids and gases. Rev. Mod. Phys. 68(4):1996;1259-1273.
7. Herrmann H.J., Luding S. Modeling granular media with the computer. Continuum Mech. Thermodyn. 10:1998;189-231.
8. A. Hansen, D. Bideau (Eds.), Disorder and Granular Media, North Holland, Amsterdam, 1992.
9. C. Thornton (Ed.), Powders and Grains 93, Balkema, Rotterdam, 1993.
10. A. Mehta (Ed.), Granular Matter, Springer, Berlin, 1994.
11. D.E. Wolf, P. Grassberger (Eds.), Friction, Arching and Contact Dynamics, World Scientific, Singapore, 1997.
12. R.P. Behringer, J.T. Jenkins (Eds.), Powders and Grains 97, Balkema, Rotterdam, 1997.
13. H.J. Herrmann, J.-P. Hovi, S. Luding (Eds.), Physics of Dry Granular Media, NATO ASI Series E 350, Kluwer Academic Publishers, Dordrecht, 1998.
14. Janssen H.A. Versuche über Getreidedruck in Silozellen. Z. Ver. Dtsch. Ing. 39(35):1895;1045-1049.
15. Liu C.-H., Nagel S.R., Schecter D.A., Coppersmith S.N., Majumdar S., Narayan O., Witten T.A. Force fluctuations in bead packs. Science. 269:1995;513.
16. Radjai F., Jean M., Moreau J.J., Roux S. Force distribution in dense two-dimensional granular systems. Phys. Rev. Lett. 77(2):1996;274.
17. Coppersmith S.N., Liu C.-H., Majumdar S., Narayan O., Witten T.A. Model for force fluctuations in bead packs. Phys. Rev. E. 53(5):1996;4673-4685.
18. S. Ouaguenouni, J.-N. Roux, Arching without friction: a simple model, in: D.E. Wolf, P. Grassberger (Eds.), Friction, Arching and Contact Dynamics, Singapore, World Scientific, 1997.
19. Hong D.C. Stress distribution of a hexagonally packed granular pile. Phys. Rev. E. 47(1):1993;760-762.
20. Liffman K., Chan D.Y.C., Hughes B.D. On the stress depression under a sandpile. Powder Technol. 78:1994;263-271.
21. Bouchaud J.-P., Cates M.E., Claudin P. Stress distribution in granular media and non-linear wave equation. J. Phys. I. 5:1995;639-656.
22. Wittmer J.-P., Cates M.E., Claudin P. Stress propagation and arching in static sandpiles. J. Phys. I. 7:1997;39-80.
23. Luding S. Stress distribution in static two dimensional granular model media in the absence of friction. Phys. Rev. E. 55(4):1997;4720-4729.
24. Matuttis H.-G. Simulations of the pressure distribution under a two dimensional heap of polygonal particles. Granular Matter. 1(2):1998;83-91.
25. Hummel F.H., Finnan E.J. The distribution of pressure on surfaces supporting a mass of granular material. Proc. Inst. Civil Eng. 212:1921;369-392. the former: Minutes of Proc. of the Instn. of Civil Engineers with other selected papers.
26. Jotaki T., Moriyama R. On the bottom pressure distribution of the bulk materials piled with the angle of repose. J. Soc. Powder Technol., Jpn. 164:1979;184-191.
27. Trollope D.H., Burman B.C. Physical and numerical experiments with granular wedges. Geotechnique. 30(2):1980;137-157.
28. Šmid J., Novosad J. Pressure distribution under heaped bulk solids. Inst. Chem. Eng. Symp. Ser. 63:1981;. D3/V/1-12.
29. Brockbank R., Huntley J.M., Ball R.C. Contact force distribution beneath a three-dimensional granular pile. J. Phys. II, France. 7:1997;1521-1532.
30. I.K. Lee, J.R. Herrington, Stresses beneath granular embarkments, Proceedings of the first Australian-New Zealand Conference on Geomechanics, Melbourne, Vol. 1, August 1971, pp. 291-296.
31. B. Lackinger, Das Tragverhalten von Staudämmen mit membranartigen Dichtungen, PhD Thesis, Mitteilungen des Instituts für Bodenmechanik, Felsmechanik und Grundbau an der Fakultät für Bauingenieurwesen und Architekture der Universität Innsbruck, 1980.
32. Cundall P.A., Strack O.D.L. A discrete numerical model for granular assemblies. Geotechnique. 29(1):1979;47-65.
33. Bathurst R.J., Rothenburg L. Micromechanical aspects of isotropic granular assemblies with linear contact interactions. J. Appl. Mech. 55:1988;17.
34. Thornton C. Force transmission in granular media. KONA. 15:1997;81-90.
35. C. Thornton, C.W. Randall, Applications of theoretical contact mechanics to solid particle system simulation, in: Micromechanics of Granular Media, Elsevier, Amsterdam, 1988.
36. Bashir Y.M., Goddard J.D. A novel simulation method for the quasi-static mechanics of granular assemblages. J. Rheol. 35(5):1991;849-885.
37. Dobry R., Ng T.T. Discrete modelling of stress-strain behaviour of granular media at small and large strains. Eng. Comput. 9:1992;129-143.
38. C. Thornton, S.J. Antony, Quasi-static deformation of particulate media, Philos. Trans. R. Soc., Ser. A (1998), submitted for publication.
39. C. Thornton, Numerical simulations of deviatoric shear deformation of granular media, Geotechnique (1998), submitted for publication.
40. Ting J.M. A robust algorithm for ellipse-based discrete element modelling of granular materials. Comput. Geotech. 13:1992;175-186.
41. L. Meachum, J.M. Ting, J.D. Rowell, Influence of particle shape on the strength of ellipse-shaped granular assemblages, in: J.R. Williams (Ed.), Proceedings on the 2nd International Conference on Discrete Element Methods (DEM), Cambridge, MA, IESL Publ., 1993, pp. 215-225.
42. T.T. Ng, Numerical simulations of granular soil using elliptical particles, Microstructural characterization in Constitutive Modeling of Metals and Granular Media, Presented at the ASME Summer Mechanics and Materials Conferences, volume MD-Vol. 32, ASME, April 28-May 1, 1992.
43. Williams J.R., Pentland A.P. Superquadrics and modal dynamics for discrete elements in interactive design. Eng. Comput. 9:1992;115-127.
44. Potapov A.V., Campbell C.S. A fast model for the simulation of non-round particles. Granular Matter. 1(1):1998;9-14.
45. Barbosa R., Ghaboussi J. Discrete finite element method. Eng. Comput. 9:1992;253-266.
46. Issa J.A., Nelson R.B. Numerical analysis of micromechanical behaviour of granular materials. Eng. Comput. 9:1992;211-223.
47. Hocking G. The discrete element method for analysis of fragmentation of discontinua. Eng. Comput. 9:1992;145-155.
48. Tillemans H.-J., Herrmann H.J. Simulating deformations of granular solids under shear. Physica A. 217:1995;261-288.
49. Kun F., Herrmann H.J. Fragmentation of colliding discs. Int. J. Mod. Phys. C. 7(6):1996;837-855.
50. Kruyt N.P., Rothenburg L. Micromechanical definition of strain tensor for granular materials. J. Appl. Mech. 118:1996;706-711.
51. Liao C.-L., Chang T.-P., Young D.-H., Chang C.S. Stress-strain relationship for granular materials based on the hypothesis of best fit. Int. J. Solids Struct. 34:1997;4087-4100.
52. M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Oxford Univ. Press, Oxford, 1987.
53. D.C. Rapaport, The Art of Molecular Dynamics Simulation, Cambridge Univ. Press, Cambridge, 1995.
54. O.R. Walton, Force models for particle-dynamics simulations of granular materials, in: E. Guazzelli, L. Oger (Eds.), Mobile Particulate Systems, Kluwer Academic Publishers, Dordrecht, 1995, p. 367.
55. Schäfer J., Dippel S., Wolf D.E. Force schemes in simulations of granular materials. J. Phys. I, France. 6:1996;5-20.
56. S. Luding, Collisions and contacts between two particles, in: H.J. Herrmann, J.-P. Hovi, S. Luding (Eds.), Physics of Dry Granular Media, NATO ASI Series E350, Kluwer Academic Publishers, Dordrecht, 1998, p. 285.
57. O.R. Walton, Numerical simulation of inelastic, frictional particle-particle interactions, in: M.C. Roco (Ed.), Particulate Two-Phase Flow, Butterworth-Heinemann, Boston, 1993, p. 884.
58. Lian G., Adams M.J., Thornton C. Elastohydrodynamic collisions of solid spheres. J. Fluid Mech. 311:1996;141.
59. Foerster S.F., Louge M.Y., Chang H., Allia K. Measurements of the collision properties of small spheres. Phys. Fluids. 6(3):1994;1108-1115.
60. Labous L., Rosato A.D., Dave R. Measurements of collision properties of spheres using high-speed video analysis. Phys. Rev. E. 56:1997;5715.
61. Falcon E., Laroche C., Fauve S., Coste C. Behavior of one inelastic ball bouncing repeatedly off the ground. Eur. Phys. J. B. 3:1998;45-57.
62. Hertz H. Über die Berührung fester elastischer Körper. J. Reine Angew. Math. 92:1882;136.
63. L.D. Landau, E.M. Lifshitz, Elasticity Theory, Pergamon, Oxford, 1975.
64. Walton O.R., Braun R.L. Viscosity, granular-temperature and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30(5):1986;949-980.
65. Thornton C. Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres. J. Appl. Mech. 64:1997;383-386.
66. Kuwabara G., Kono K. Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys. 26(8):1987;1230-1233.
67. Luding S., Clément E., Blumen A., Rajchenbach J., Duran J. Anomalous energy dissipation in molecular dynamics simulations of grains: the "detachment effect" Phys. Rev. E. 50:1994;4113.
68. Brilliantov N.V., Spahn F., Hertzsch J.M., Pöschel T. Model for collisions in granular gases. Phys. Rev. E. 53(5):1996;5382.
69. Lee J., Herrmann H.J. Angle of repose and angle of marginal stability: molecular dynamics of granular particles. J. Phys. A. 26:1993;373.
70. L. Brendel, S. Dippel, Lasting contacts in molecular dynamics simulations, in: H.J. Herrmann, J.-P. Hovi, S. Luding (Eds.), Physics of Dry Granular Media, Kluwer Academic Publishers, Dordrecht, 1998, p. 313.
71. Radjai F., Schäfer J., Dippel S., Wolf D. Collective friction of an array of particles: a crucial test for numerical algorithms. J. Phys. I, France. 7:1997;1053.
72. O.R. Walton, R.L. Braun, Simulation of rotary-drum and repose tests for frictional spheres and rigid sphere clusters, DOE/NSF Workshop on Flow of Particulates and Fluids, 1993, pp. 1-17.
73. Buchholtz V., Pöschel T., Tillemans H.-J. Simulation of rotating drum experiments using non-circular particles. Physica A. 216:1995;199.
74. Buchholtz V., Pöschel T. Numerical investigations of the evolution of sandpiles. Physica A. 202:1994;390.
75. Kohring G.A., Melin S., Puhl H., Tillemans H.J., Vermöhlen W. Computer simulations of critical, non-stationary granular flow through a hopper. Comput. Methods Appl. Mech. Eng. 124:1995;2273.
76. H.-G. Matuttis, S. Luding, The effect of particle shape and friction on the stresses in heaps of granular media, in: D.E. Wolf, P. Grassberger (Eds.), Friction, Arching and Contact Dynamics, World Scientific, Singapore, 1997.
77. Shi G.-H. Discontinous deformation analysis: a new numerical model for the statics and dynamics of deformable block structures. Eng. Comput. 9:1992;157-168.
78. Krishnasamy J., Jakiela M.J. A method to resolve ambiguities in corner-corner interactions between polygons in the context of motion simulations. Eng. Comput. 12:1995;135-144.
79. Pöschel T., Buchholtz V. Molecular dynamics of arbitrarily shaped granular particles. J. Phys. I, France. 5(11):1995;1431-1455.
80. Munjiza A., Owen D.R.J., Bicanic N. A combined finite-discrete element method in transient dynamics of fracturing solids. Eng. Comput. 12:1995;145-174.
81. H.-J. Tillemanns, Molekulardynamik beliebig geformter Teilchen in zwei Dimensionen, PhD Thesis, Universität Köln, 1995.
82. J.D. Goddard, Microstructural origins of continuum stress fields-a brief history and some unresolved issues, in: D. DeKee, P.N. Kaloni (Eds.), Recent Developments in Structured Continua, Pitman Research Notes in Mathematics, No. 143, Wiley, Longman, New York, 1986, p. 179.
83. Liffman K., Chan D.Y.C., Hughes B.D. Force distribution in a two dimensional sandpile. Powder Technol. 72:1992;255-267.
84. S. van Baars, Discrete Element Analysis of Granular Materials, PhD Thesis, Technische Universiteit Delft, Delft, Nederlands, 1996.
85. Oron G., Herrmann H.J. Exact calculation of force networks in granular media. Phys. Rev. E. 582:1998;2079-2089. cond-mat/9707243.
86. Wittmer J.P., Claudin P., Cates M.E., Bouchaud J.-P. An explanation for the central stress minimum in sand piles. Nature. 382:1996;336-338.
87. S. Luding, H.-G. Matuttis, The effect of interaction laws on the stresses in frictionless granular media, in: D.E. Wolf, P. Grassberger (Eds.), Friction, Arching and Contact Dynamics, World Scientific, Singapore, 1997, pp. 207-211.
88. Edwards S.F., Mounfield C.C. A theoretical model for the stress distribution in granular matter: III. Forces in sandpiles. Physica A. 226:1996;25.
89. G. Oron, H.J. Herrmann, Exact determination of force networks in a static assembly of disks, in: H.J. Herrmann, J.-P. Hovi, S. Luding (Eds.), Physics of Dry Granular Media, Kluwer Academic Publishers, Dordrecht, 1998, p. 143.
90. Hemmingsson J., Herrmann H.J., Roux S. On stress networks in granular media. J. Phys. I. 7:1997;291-302.