Cohesive, frictional powders: Contact models for tension. (English) Zbl 1304.74019
Summary: The contacts between cohesive, frictional particles with sizes in the range \(0.1-10 \mu m\) are the subject of this study. Discrete element model (DEM) simulations rely on realistic contact force models-however, too much details make both implementation and interpretation prohibitively difficult. A rather simple, objective contact model is presented, involving the physical properties of elastic-plastic repulsion, dissipation, adhesion, friction as well as rolling- and torsion-resistance. This contact model allows to model bulk properties like friction, cohesion and yield-surfaces. Very loose packings and even fractal agglomerates have been reported in earlier work. The same model also allows for pressure-sintering and tensile strength tests as presented in this study.
Keywords:
granular materials; molecular dynamics (MD) and discrete elementmodel (DEM) force-laws; friction; rolling- and torsion-resistance; adhesion; plastic deformationReferences:
| [1] | Allen M.P. and Tildesley D.J. (1987). Computer Simulation of Liquids. Oxford University Press, Oxford · Zbl 0703.68099 |
| [2] | Bartels G., Unger T., Kadau D., Wolf D.E. and Kertesz J. (2005). The effect of contact torques on porosity of cohesive powders. Granular Matter 7: 139 · Zbl 1094.74016 · doi:10.1007/s10035-004-0184-8 |
| [3] | Bashir Y.M. and Goddard J.D. (1991). A novel simulation method for the quasi-static mechanics of granular assemblages. J Rheol 35(5): 849–885 · doi:10.1122/1.550160 |
| [4] | Berger, F.: Das Gesetz des Kraftverlaufes beim Stoß. Friedr. Vieweg & Sohn AG (1924) |
| [5] | Brendel L. (2006). Modeling of caked contacts in DEMs. Chem Eng Technol 29(11): 1355–1359 · doi:10.1002/ceat.200600132 |
| [6] | Brendel, L., Dippel, S.: Lasting contacts in molecular dynamics simulations. In: Herrmann, H.J., Hovi, J.P., Luding, S. (eds) Physics of Dry Granular Media. Kluwer, Dordrecht, p 313 (1998) |
| [7] | Brilliantov N.V., Spahn F., Hertzsch J.M. and Pöschel T. (1996). Model for collisions in granular gases. Phys Rev E 53(5): 5382 · doi:10.1103/PhysRevE.53.5382 |
| [8] | Butt H.J., Cappella B. and Kappl M. (2005). Force measurements with the atomic force microscope: Technique, interpretation and applications. Surf. Sci. Rep. 59(1–6): 1–152 · doi:10.1016/j.surfrep.2005.08.003 |
| [9] | Castellanos A. (2005). The relationship between attractive interparticle forces and bulk behavior in dry and uncharged fine powders. Adv. Phys. 54(4): 263–376 · doi:10.1080/17461390500402657 |
| [10] | Coste, C., Falcon, E., Fauve, S.: Propagations d’ondes non-linéaires dans une chaîne de bille s en contact de Hertz. In: Petit C., Pijaudier-Cabot G., Reynouard J.M. (eds) Des géomatériaux aux ouvrages: expérimentations et modélis ations, Hermes, Paris, pp 33–52 (in french, 1995) |
| [11] | Coste C., Falcon E. and Fauve S. (1997). Solitary waves in a chain of beads under Hertz contact. Phys. Rev. E 56(5): 6104–6117 · doi:10.1103/PhysRevE.56.6104 |
| [12] | Cundall P.A. and Strack O.D.L. (1979). A discrete numerical model for granular assemblies. Géotechnique 29(1): 47–65 · doi:10.1680/geot.1979.29.1.47 |
| [13] | David, C.T., Rojo, R.G., Herrmann, H.J., Luding, S.: Hysteresis and creep in powders and grains. In: Garcia-Rojo, R., Herrmann, H.J., McNamara, S. (eds) Powders and Grains 2005, Balkema, Leiden, Netherlands, pp. 291–294 (2005) |
| [14] | David C.T., Garcia-Rojo R., Herrmann H.J. and Luding S. (2007). Powder flow testing with 2d and 3d biaxial and triaxial simulations. Particle Particle Syst. Charact. 24(1): 29–33 · doi:10.1002/ppsc.200601052 |
| [15] | Derjaguin B.V., Muller V.M. and Toporov Y.P. (1975). Effect of contact deformation on adhesion of particles. J. Colloid Interf. Sci. 53: 314–326 · doi:10.1016/0021-9797(75)90018-1 |
| [16] | Dintwa E., van Zeebroeck M., Tijskens E. and Ramon H. (2005). Torsion of viscoelastic spheres in contact. Granular Matter 7(2–3): 169–179 · Zbl 1146.74035 · doi:10.1007/s10035-005-0207-0 |
| [17] | Els, D.: Definition of roll velocity for spherical particles. Granular Matter (2006, submitted) |
| [18] | Foerster S.F., Louge M.Y., Chang H. and Allia K. (1994). Measurements of the collision properties of small spheres. Phys. Fluids 6(3): 1108–1115 · doi:10.1063/1.868282 |
| [19] | Grof Z., Lawrence C.J. and Stepanek F. (2008). Computer simulation of evolving capillary bridges in granular media. Granular Matter 10(2): 93–103 · Zbl 1258.76181 · doi:10.1007/s10035-007-0071-1 |
| [20] | Heim L.O., Butt H.J., Blum J. and Schrapler R. (2008). A new method for the analysis of compaction processes in high-porosity agglomerates. Granular Matter 10(2): 89–91 · doi:10.1007/s10035-007-0072-0 |
| [21] | Herrmann, H.J., Hovi, J.P., Luding, S.: (eds) Physics of dry granular media–NATO ASI Series E 350. Kluwer, Dordrecht (1998) · Zbl 0926.74003 |
| [22] | Hertz H. (1882). Über die Berührung fester elastischer K örper. J für die reine u angew Math 92: 136 |
| [23] | Janssen H.A. (1895). Versuche über Getreidedruck in Silozellen. Zeitschr d Vereines deutscher Ingenieure 39(35): 1045–1049 |
| [24] | Jenkins J.T. and Koenders M.A. (2005). Hydrodynamic interaction of rough spheres. Granular Matter 7(1): 13–18 · Zbl 1095.76054 · doi:10.1007/s10035-004-0193-7 |
| [25] | Johnson K.L. (1989). Contact Mechanics. Cambridge University Press, Cambridge · Zbl 0599.73108 |
| [26] | Johnson K.L., Kendall K. and Roberts A.D. (1971). Surface energy and contact of elastic solids. Proc R Soc Lond Ser A 324(1558): 301 · doi:10.1098/rspa.1971.0141 |
| [27] | Johnson P.C. and Jackson R. (1987). Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J Fluid Mech 176: 67 · doi:10.1017/S0022112087000570 |
| [28] | Kadau D., Schwesig D., Theuerkauf J. and Wolf D.E. (2006). Influence of particle elasticity in shear testers. Granular Matter 8: 34–40 · doi:10.1007/s10035-005-0217-y |
| [29] | Kafui K.D. and Thornton C. (2000). Numerical simulations of impact breakage of spherical crystalline agglomerate. Powder Technol 109: 113–132 · doi:10.1016/S0032-5910(99)00231-4 |
| [30] | Kappl, M., Heim, L., Butt, H.J., Luding, S., Tykhoniuk, R., Tomas, J.: From grains to powders: from single particle contact mechanics measurements to bulk powder properties. In: Garcia-Rojo, R., Herrmann, H.J., McNamara, S. (eds) Powders and Grains 2005, Balkema, Leiden, Netherlands, pp. 493–497 (2005) |
| [31] | Kun F. and Herrmann H.J. (2000). Damage development under gradual loading of composites. J. Mater. Sci. 35(18): 4685–4693 · doi:10.1023/A:1004842704921 |
| [32] | Kuwabara G. and Kono K. (1987). Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys. 26(8): 1230–1233 · doi:10.1143/JJAP.26.1230 |
| [33] | Labous L., Rosato A.D. and Dave R. (1997). Measurements of collision properties of spheres using high-speed video analysis. Phys. Rev. E 56: 5715 · doi:10.1103/PhysRevE.56.5717 |
| [34] | Lätzel M., Luding S., Herrmann H.J., Howell D.W. and Behringer R.P. (2003). Comparing simulation and experiment of a 2d granular couette shear device. Eur. Phys. J. Eng. 11(4): 325–333 · doi:10.1140/epje/i2002-10160-7 |
| [35] | Leroy B. (1985). Collision between two balls accompanied by deformation: A qualitative approach to Hertz’s theory. Am. J. Phys. 53(4): 346–349 · doi:10.1119/1.14164 |
| [36] | Lian G., Adams M.J. and Thornton C. (1996). Elastohydrodynamic collisions of solid spheres. J Fluid. Mech. 311: 141 · Zbl 0858.73015 · doi:10.1017/S0022112096002534 |
| [37] | Lorenz A., Tuozzolo C. and Louge M.Y. (1997). Measurements of impact properties of small, nearly spherical particles. Exp. Mech. 37(3): 292–297 · doi:10.1007/BF02317421 |
| [38] | Lubachevsky B.D. (1991). How to simulate billards and similar systems. J. Comp. Phys. 94(2): 255 · Zbl 0716.68094 · doi:10.1016/0021-9991(91)90222-7 |
| [39] | Luding S. (1998). Collisions and contacts between two particles. In: Herrmann, H.J., Hovi, J.P. and Luding, S. (eds) Physics of dry granular media–NATO ASI Series E350, pp 285. Kluwer, Dordrecht |
| [40] | Luding, S.: Micro-macro models for anisotropic granular media. In: Vermeer, P.A., Ehlers, W., Herrmann, H.J., Ramm, E. (eds) Modelling of cohesive-frictional Materials, Balkema, pp 195–206 (ISBN 04 1536 023 4) (2004a) · Zbl 1112.74364 |
| [41] | Luding S. (2004b). Molecular dynamics simulations of granular materials. In: Hinrichsen, H. and Wolf, D.E. (eds) The Physics of Granular Media, pp 299–324. Weinheim, Wiley VCH |
| [42] | Luding S. (2005). Anisotropy in cohesive, frictional granular media. J. Phys. Condens. Matter 17: S2623–S2640 · doi:10.1088/0953-8984/17/24/017 |
| [43] | Luding, S.: About contact force-laws for cohesive frictional materials in 2d and 3d. In: Walzel, P., Linz, S., Krülle, C., Grochowski, R. (eds) Behavior of Granular Media, Shaker Verlag, pp 137–147, band 9, Schriftenreihe Mechanische Verfahrenstechnik, ISBN 3-8322-5524-9 (2006) |
| [44] | Luding, S.: Contact models for very loose granular materials. In: Eberhard P. (ed) Symposium on Multiscale Problems in Multibody System Contacts, Springer, Heidelberg, pp. 135–150. ISBN 978-1-4020-5980-3 (2007) · Zbl 1208.74024 |
| [45] | Luding, S., Herrmann, H.J.: Micro-macro transition for cohesive granular media. In: Diebels S. (Ed.) Bericht Nr. II-7, Inst. für Mechanik, Universität Stuttgart (2001) |
| [46] | Luding, S., Suiker, A.: Self-healing of damaged particulate materials through sintering. Philos. Mag. (2008, submitted) |
| [47] | Luding S., Clément E., Blumen A., Rajchenbach J. and Duran J. (1994). Anomalous energy dissipation in molecular dynamics simulations of grains: The ”detachment effect”. Phys. Rev. E 50: 4113 · doi:10.1103/PhysRevE.50.4113 |
| [48] | Luding S., Clément E., Blumen A., Rajchenbach J. and Duran J. (1994). The onset of convection in molecular dynamics simulations of grains. Phys. Rev. E 50: R1762 · doi:10.1103/PhysRevE.50.R1762 |
| [49] | Luding S., Clément E., Blumen A., Rajchenbach J. and Duran J. (1994). Studies of columns of beads under external vibrations. Phys. Rev. E 49(2): 1634 · doi:10.1103/PhysRevE.49.1634 |
| [50] | Luding S., Manetsberger K. and Muellers J. (2005). A discrete model for long time sintering. J. Mech. Phys. Solids 53(2): 455–491 · Zbl 1146.74313 · doi:10.1016/j.jmps.2004.07.001 |
| [51] | Luding, S., Suiker, A., Kadashevich, I.: Discrete element modeling of self-healing processes in damaged particulate materials. In: Schmets, A.J.M., van der Zwaag, S. (eds) Proceedings of the 1st International Conference on Self Healing Materials, Springer series in Material Science, Berlin, Germany (ISBN 978-1-4020-6249-0 (2007) |
| [52] | Matuttis H.G., Luding S. and Herrmann H.J. (2000). Discrete element methods for the simulation of dense packings and heaps made of spherical and non-spherical particles. Powder Technol. 109: 278–292 · doi:10.1016/S0032-5910(99)00243-0 |
| [53] | Mindlin R.D. (1949). Compliance of elastic bodies in contact. J. Appl. Mech. 16: 259 · Zbl 0034.26602 |
| [54] | Mindlin R.D. and Deresiewicz H. (1953). Elastic spheres in contact under varying oblique forces. J. Appl. Mech. 20: 327 · Zbl 0051.41202 |
| [55] | Moreau, J.J.: New computation methods in granular dynamics. In: Powders and Grains, vol. 93. Balkema, Rotterdam, p 227 (1993) |
| [56] | Moreau J.J. (1994). Some numerical methods in multibody dynamics: application to granular materials. Eur J Mech A 13: 93 · Zbl 0815.73009 |
| [57] | Oda M. and Iwashita K. (2000). Study on couple stress and shear band development in granular media based on numerical simulation analyses. Int. J. Eng. Sci. 38: 1713–1740 · doi:10.1016/S0020-7225(99)00132-9 |
| [58] | Oda M. and Kazama H. (1998). Microstructure of shear bands and its relation to the mechanism of dilatancy and failure of dense granular soils. Géotechnique 48(4): 465–481 · doi:10.1680/geot.1998.48.4.465 |
| [59] | Oda, M., Iwashita, K., Kazama, H.: Micro-structure developed in shear bands of dense granular soils and its computer simulation–mechanism of dilatancy and failure. In: Fleck, N.A., Cocks, A.C.E. (eds) IUTAM Symposium on Mechanics of Granular and Porous Materials. Kluwer, Dordrecht, pp 353–364 (1997) |
| [60] | Pao Y.H. (1955). Extension of the Hertz theory of impact to the viscoelastic case. J. Appl. Phys. 26: 1083 · Zbl 0067.41702 · doi:10.1063/1.1722155 |
| [61] | Pöschel T. and Schwager T. (2005). Computational Granular Dynamics. Springer, Berlin |
| [62] | Pöschel T., Schwager T. and Brilliantov N.V. (1999). Rolling friction of a hard cylinder on a viscous plane. Eur. J. Phys. 10: 169–175 |
| [63] | Radjai F., Jean M., Moreau J.J. and Roux S. (1996). Force distribution in dense two-dimensional granular systems. Phys. Rev. Lett. 77(2): 274 · doi:10.1103/PhysRevLett.77.274 |
| [64] | Radjai F., Schäfer J., Dippel S. and Wolf D. (1997). Collective friction of an array of particles: A crucial test for numerical algorithms. J. Phys. I France 7: 1053 · doi:10.1051/jp1:1997109 |
| [65] | Radjai F., Wolf D.E., Jean M. and Moreau J.J. (1998). Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80(1): 61–64 · doi:10.1103/PhysRevLett.80.61 |
| [66] | Raman C.V. (1918). The photographic study of impact at minimal velocities. Phys. Rev. 12: 442–447 · doi:10.1103/PhysRev.12.442 |
| [67] | Rapaport D.C. (1995). The Art of Molecular Dynamics Simulation. Cambridge University Press, Cambridge · Zbl 1098.81009 |
| [68] | Richefeu V., Radjai F. and Youssoufi M.S.E. (2006). Stress transmission in wet granular materials. Eur. Phys. J. Eng. 21(4): 359–369 · doi:10.1140/epje/i2006-10077-1 |
| [69] | Röck M., Morgeneyer M., Schwedes J., Brendel L., Wolf D.E. and Kadau D. (2008). Visualization of shear motions of cohesive powders in the true biaxial shear tester. Partic. Sci. Technol. 26: 43–54 · doi:10.1080/02726350701759233 |
| [70] | Roux, S.: Quasi-static contacts. In: Herrmann, H.J., Hovi, J.P., Luding, S. (eds) Physics of dry granular media–NATO ASI Series E 350, Kluwer, Dordrecht, p. 267 (1998) |
| [71] | Sadd M.H., Tai Q.M. and Shukla A. (1993). Contact law effects on wave propagation in particulate materials using distinct element modeling. Int. J. Non-Lin. Mech. 28(2): 251 · Zbl 0800.73054 · doi:10.1016/0020-7462(93)90061-O |
| [72] | Savkoor A.R. and Briggs G.A.D. (1977). The effect of tangential force on the contact of elastic solids in adhesion. Proc. R. Soc. Lond. A 356: 103 · Zbl 0364.73095 · doi:10.1098/rspa.1977.0123 |
| [73] | Schäfer J., Dippel S. and Wolf D.E. (1996). Force schemes in simulations of granular materials. J. Phys. I France 6: 5–20 · doi:10.1051/jp1:1996129 |
| [74] | Severens I.E.M., de Ven A.A.F.V., Wolf D.E. and Mattheij R.M.M. (2006). Discrete element method simulations of toner behavior in the development nip of the oce direct imaging print process. Granular Matter 8(3–4): 137–150 · Zbl 1106.78009 · doi:10.1007/s10035-006-0010-6 |
| [75] | Sinkovits R.S. and Sen S. (1995). Nonlinear dynamics in granular columns. Phys. Rev. Lett. 74(14): 2686 · doi:10.1103/PhysRevLett.74.2686 |
| [76] | Spahn F., Hertzsch J.M. and Brilliantov N.V. (1995). The role of particle collisions for the dynamics in planetary rings. Chaos Solitons Fractals 5: 1945 · doi:10.1016/0960-0779(94)00195-V |
| [77] | Sperl M. (2006). Experiments on corn pressure in silo cells. Translation and comment of Janssen’s paper from 1895. Granular Matter 8(2): 59–65 · Zbl 1178.74003 · doi:10.1007/s10035-005-0224-z |
| [78] | Suiker A.S.J. and Fleck N.A. (2004). Frictional collapse of granular assemblies. J. Appl. Mech. 71: 350–358 · Zbl 1111.74650 · doi:10.1115/1.1753266 |
| [79] | Tanakov M.Y., Trusov L.I., Belyi M.V., Bulgakov V.E. and Gryaznov V.G. (1993). Elastically stressed state in small particles under conditions of Hertzian contacts. J. Phys. D 26: 997 · doi:10.1088/0022-3727/26/6/018 |
| [80] | Thornton C. (1997). Force transmission in granular media. KONA Powder Particle 15: 81–90 |
| [81] | Thornton C. (2000). Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1): 43–53 · doi:10.1680/geot.2000.50.1.43 |
| [82] | Thornton C. and Antony S.J. (2000). Quasi-static deformation of a soft particle system. Powder Technol. 109(1–3): 179–191 · doi:10.1016/S0032-5910(99)00235-1 |
| [83] | Thornton, C., Randall, C.W.: Applications of theoretical contact mechanics to solid particle system simulation. In: Micromechanics of granular media. Elsevier, Amsterdam (1988) |
| [84] | Thornton C. and Yin K.K. (1991). Impact of elastic spheres with and without adhesion. Powder Technol. 65: 153 · doi:10.1016/0032-5910(91)80178-L |
| [85] | Thornton, C., Zhang, L.: A DEM comparison of different shear testing devices. In: Kishino, Y. (ed) Powders and Grains 2001. Balkema, Rotterdam, pp. 183–190 (2001) |
| [86] | Tighe B.P. and Sperl M. (2007). Pressure and motion of dry sand: translation of Hagen’s paper from 1852. Granular Matter 9(3/4): 141–144 · doi:10.1007/s10035-006-0027-x |
| [87] | Tomas J. (2000). Particle adhesion fundamentals and bulk powder consolidation. KONA 18: 157–169 |
| [88] | Tomas J. (2004). Fundamentals of cohesive powder consolidation and flow. Granular Matter 6(2/3): 75–86 · Zbl 1101.74023 · doi:10.1007/s10035-004-0167-9 |
| [89] | Tykhoniuk R., Tomas J. and Luding S. (2006). A microstructure-based simulation environment on the basis of an interface enhanced particle model. Granular Matter 8(3/4): 159–174 · Zbl 1200.74028 · doi:10.1007/s10035-006-0004-4 |
| [90] | Valverde J.M. and Castellanos A. (2007). Compaction of fine powders: from fluidized agglomerates to primary particles. Granular Matter 9(1–2): 19–24 · doi:10.1007/s10035-006-0022-2 |
| [91] | Vermeer, P.A., Diebels, S., Ehlers, W., Herrmann, H.J., Luding, S., Ramm, E. (eds) Continuous and Discontinuous Modelling of Cohesive Frictional Materials. Lecture Notes in Physics, vol. 568. Springer, Berlin (2001) · Zbl 0958.00017 |
| [92] | Vermeer, P.A., Ehlers, W., Herrmann, H.J., Ramm, E.: (eds) Modelling of Cohesive-frictional materials, Balkema, Leiden, Netherlands (ISBN 04 1536 023 4) (2004) · Zbl 0958.00017 |
| [93] | Walton K. (1978). The oblique compression of two elastic spheres. J. Mech. Phys. Solids 26: 139 · Zbl 0384.73082 · doi:10.1016/0022-5096(78)90005-4 |
| [94] | Walton O.R. (1989). Force models for particle-dynamics simulations of granular materials. NATO ASI Ser. E Appl. Sci. 287: 367–379 |
| [95] | Walton, O.R.: Effects of interparticle friction and particle shape on dynamic angles of repose via particle-dynamics simulation. In: Workshop: Mechanics and Statistical Physics of Particulate Materials (1994) |
| [96] | Walton, O.R.: Elastic frictional contact models based on analysis of Mindlin (1949), private communication (1995a) |
| [97] | Walton O.R. (1995). Force models for particle-dynamics simulations of granular materials. In: Guazzelli, E. and Oger, L. (eds) Mobile particulate systems, pp 367. Kluwer, Dordrecht |
| [98] | Walton O.R. and Braun R.L. (1986). Viscosity, granular-temperature and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30(5): 949–980 · doi:10.1122/1.549893 |
| [99] | Zhu C.Y., Shukla A. and Sadd M.H. (1991). Prediction of dynamic contact loads in granular assemblies. J. Appl. Mech. 58: 341 · doi:10.1115/1.2897191 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
