Modeling force transmission in granular materials

Farhang Radjai

doi:10.1016/j.crhy.2015.01.003

Modeling force transmission in granular materials

Farhang Radjai ^1,²

¹ LMGC, UMR 5509 CNRS – University of Montpellier, place Eugène-Bataillon, 34095 Montpellier, France
² MultiScale Material Science for Energy and Environment, UMI 3466 CNRS–MIT, CEE, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge 02139, USA

Comptes Rendus. Physique, Granular physics / Physique des milieux granulaires, Volume 16 (2015) no. 1, pp. 3-9.

Abstract
Résumé

The probability density function of contact forces in granular materials has been extensively studied and modeled as an outstanding signature of granular microstructure. Arguing that particle environments play a fundamental role in force transmission, we analyze the effects of steric constraints with respect to force balance condition and show that each force may be considered as resulting from a balance between lower and larger forces in proportions that mainly depend on steric effects. This idea leads to a general model that predicts an analytical expression of force density with a single free parameter. This expression fits well our simulation data and generically predicts the exponential fall-off of strong forces, a small peak below the mean force and the non-zero probability of vanishingly small forces.

La densité de probabilité des forces de contact dans les matériaux granulaires représente une signature remarquable de la microstructure granulaire et, à ce titre, elle a fait l'objet de nombreuses études et d'efforts de modélisation. Nous allons analyser le rôle fondamental des environnementaux locaux des particules pour la transmission des forces et les effets des contraintes stériques par rapport à l'équilibre des forces. Cette analyse permet de montrer qu'une force de contact met en jeu des forces supérieures et inférieures à cette force dans des proportions qui sont contrôlées par les effets stériques. Cette idée simple conduit à un modèle général qui prédit une expression analytique de la densité des forces avec un seul paramètre libre. Ce paramètre coïncide avec le degré d'homogénéité des forces et peut dépendre de l'anisotropie du réseau des contacts ou des formes et distributions des tailles des particules. Cette expression ajuste bien les données numériques et prédit d'une manière générique la décroissance exponentielle des forces fortes, un petit pic en dessous de la force moyenne et une densité de probabilité non nulle pour les forces très petites.

Published online: 2015-01-01

DOI: 10.1016/j.crhy.2015.01.003

Keywords: Granular matter, Force chains, Arching, Contact dynamics, Molecular dynamics
Mots-clés : Matière granulaire, Chaînes de force, Effet de voûte, Exclusions stériques, Dynamique des contacts, Dynamique moléculaire

Author's affiliations:

Farhang Radjai ^{1, 2}

¹ LMGC, UMR 5509 CNRS – University of Montpellier, place Eugène-Bataillon, 34095 Montpellier, France
² MultiScale Material Science for Energy and Environment, UMI 3466 CNRS–MIT, CEE, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge 02139, USA

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     author = {Farhang Radjai},
     title = {Modeling force transmission in granular materials},
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     doi = {10.1016/j.crhy.2015.01.003},
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Farhang Radjai. Modeling force transmission in granular materials. Comptes Rendus. Physique, Granular physics / Physique des milieux granulaires, Volume 16 (2015) no. 1, pp. 3-9. doi : 10.1016/j.crhy.2015.01.003. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2015.01.003/

References
Cited by

[1] P. Dantu Contribution à l'étude mécanique et géométrique des milieux pulvérulents, Proc. of the 4th International Conf. on Soil Mech. and Foundation Eng., vol. 1, Butterworths Scientific Publications, London, 1957, pp. 144-148

[2] A. Drescher; G. de Josselin de Jong Photoelastic verification of a mechanical model for the flow of a granular material, J. Mech. Phys. Solids, Volume 20 (1972), pp. 337-351

[3] T. Travers; M. Ammi; D. Bideau; A. Gervois; J.-C. Messager; J.-P. Troadec Uniaxial compression of 2d packings of cylinders. Effects of weak disorder, Europhys. Lett., Volume 4 (1987) no. 3, pp. 329-332

[4] C. Liu; S.R. Nagel; D.A. Schecter; S.N. Coppersmith; S. Majumdar; O. Narayan; T.A. Witten Force fluctuations in bead packs, Science, Volume 269 (1995), p. 513

[5] F. Radjai; M. Jean; J.-J. Moreau; S. Roux Force distributions in dense two-dimensional granular systems, Phys. Rev. Lett., Volume 77 (1996) no. 2, p. 274

[6] C. Thornton Force transmission in granular media, KONA Powder Part., Volume 15 (1997), pp. 81-90

[7] O. Tsoungui; D. Vallet; J.-C. Charmet Use of contact area trace to study the force distributions inside 2d granular systems, Granul. Matter, Volume 1 (1998) no. 2, pp. 65-69

[8] D.M. Mueth; H.M. Jaeger; S.R. Nagel Force distribution in a granular medium, Phys. Rev. E, Volume 57 (1998), p. 3164

[9] G. Lovol; K. Maloy; E. Flekkoy Force measurements on static granular materials, Phys. Rev. E, Volume 60 (1999), pp. 5872-5878

[10] F. Radjai; S. Roux; J.J. Moreau Contact forces in a granular packing, Chaos, Volume 9 (1999) no. 3, pp. 544-550

[11] S.G. Bardenhagen; J.U. Brackbill; D. Sulsky Numerical study of stress distribution in sheared granular material in two dimensions, Phys. Rev. E, Volume 62 (2000), pp. 3882-3890

[12] L.E. Silbert; G.S. Grest; J.W. Landry Statistics of the contact network in frictional and frictionless granular packings, Phys. Rev. E, Volume 66 (2002), pp. 1-9

[13] T.S. Majmudar; R.P. Behringer Contact force measurements and stress-induced anisotropy in granular materials, Nature, Volume 435 (2005), pp. 1079-1082

[14] D.L. Blair; N.W. Mueggenburg; A.H. Marshall; H.M. Jaeger; S.R. Nagel Force distributions in three-dimensional granular assemblies: effects of packing order and interparticle friction, Phys. Rev. E, Volume 63 (2001), p. 041304

[15] E. Azéma; F. Radjai; R. Peyroux; G. Saussine Force transmission in a packing of pentagonal particles, Phys. Rev. E, Volume 76 (2007) no. 1 Pt 1, p. 011301

[16] V. Richefeu; M.S. El Youssoufi; E. Azéma; F. Radjai Force transmission in dry and wet granular media, Powder Technol., Volume 190 (2009), pp. 258-263

[17] E. Azéma; G. Saussine; F. Radjai Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles, Mech. Mater., Volume 41 (2009), pp. 729-741

[18] T. Travers; M. Ammi; D. Bideau; A. Gervois; J.-C. Messager; J.-P. Troadec Mechanical size effects in 2d granular media, J. Phys. France, Volume 49 (1988), pp. 939-948

[19] O. Tsoungui; D. Vallet; J.-C. Charmet; S. Roux “Partial pressures” supported by granulometric classes in polydisperse granular media, Phys. Rev. E, Volume 57 (1998) no. 4, pp. 4458-4465

[20] F. Radjai; D.E. Wolf The origin of static pressure in dense granular media, Granul. Matter, Volume 1 (1998), pp. 3-8

[21] S.J. Antony Evolution of force distribution in three-dimensional granular media, Phys. Rev. E, Volume 63 (2001) no. 1 Pt 1, p. 011302

[22] F. Radjai; D.E. Wolf; M. Jean; J. Moreau Bimodal character of stress transmission in granular packings, Phys. Rev. Lett., Volume 80 (1998), pp. 61-64

[23] C.S. O'Hern; S.A. Langer; A.J. Liu; S.R. Nagel Force distributions near jamming and glass transitions, Phys. Rev. Lett., Volume 86 (2001) no. 1, pp. 111-114

[24] J.H. Snoeijer; T.J.H. Vlugt; M. van Hecke; W. van Saarloos Force network ensemble: a new approach to static granular matter, Phys. Rev. Lett., Volume 92 (2004) no. 5, p. 054302

[25] P.T. Metzger Comment on “Mechanical analog of temperature for the description of force distribution in static granular packings”, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., Volume 69 (2004) no. 5 Pt 1, p. 053301 (discussion 053302)

[26] P.T. Metzger Granular contact force density of states and entropy in a modified Edwards ensemble, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., Volume 70 (2004) no. 5 Pt 1, p. 051303

[27] E. Azéma; F. Radjai Internal structure of inertial granular flows, Phys. Rev. Lett., Volume 112 (2014) no. 7, p. 078001

[28] C. Voivret; F. Radjai; J.-Y. Delenne; M.E. Youssoufi Force transmission in polydisperse granular media, Phys. Rev. Lett., Volume 102 (2009), p. 178001

[29] B. Saint-Cyr; J.-Y. Delenne; C. Voivret; F. Radjai; P. Sornay Rheology of granular materials composed of nonconvex particles, Phys. Rev. E, Volume 84 (2011) no. 4, p. 041302

[30] E. Azema; F. Radjai; B. Saint-Cyr; J.-Y. Delenne; P. Sornay Rheology of 3d packings of aggregates: microstructure and effects of nonconvexity, Phys. Rev. E, Volume 87 (2013), p. 052205

[31] D.-H. Nguyen; E. Azéma; F. Radjai; P. Sornay Effect of size polydispersity versus particle shape in dense granular media, Phys. Rev. E, Volume 90 (2014) no. 1, p. 012202

[32] E.I. Corwin; H.M. Jaeger; S.R. Nagel Structural signature of jamming in granular media, Nature, Volume 435 (2005) no. 7045, pp. 1075-1078

[33] S.N. Coppersmith; C. Liu; S. Majumdar; O. Narayan; T.A. Witten Model for force fluctuations in bead packs, Phys. Rev. E, Volume 53 (1996) no. 5, pp. 4673-4685

[34] J. Goddard On entropy estimates of contact forces in static granular assemblies, Int. J. Solids Struct., Volume 41 (2004) no. 21, pp. 5851-5861

[35] R. Youngquist; P. Metzger; K. Kilts Force density function relationships in 2-d granular media, SIAM J. Appl. Math., Volume 65 (2005) no. 6, pp. 1855-1869

[36] I. Agnolin; J.-N. Roux Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., Volume 76 (2007) no. 6–1, p. 061302

[37] J. Moreau Some numerical methods in multibody dynamics: application to granular, Eur. J. Mech. A, Solids, Volume 13 (1994), pp. 93-114

[38] F. Radjai; V. Richefeu Contact dynamics as a nonsmooth discrete element method, Mech. Mater., Volume 41 (2009), pp. 715-728

[39] F. Radjai; L. Brendel; S. Roux Nonsmoothness, indeterminacy, and friction in two-dimensional arrays of rigid particle, Phys. Rev. E, Volume 54 (1996) no. 1, p. 861

[40] J.H. Snoeijer; T.J.H. Vlugt; W.G. Ellenbroek; M. van Hecke; J.M.J. van Leeuwen Ensemble theory for force networks in hyperstatic granular matter, Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., Volume 70 (2004) no. 6 Pt 1, p. 061306

[41] F. Radjai; J.-Y. Delenne; É. Azema; S. Roux Fabric evolution and accessible geometrical states in granular materials, Granul. Matter, Volume 14 (2012) no. 2, pp. 259-264

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