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Some explicit expressions for the probability distribution of force magnitude

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Abstract

Recently, empirical investigations have suggested that the components of contact forces follow the exponential distribution. However, explicit expressions for the probability distribution of the corresponding force magnitude have not been known and only approximations have been used in the literature. In this note, for the first time, I provide explicit expressions for the probability distribution of the force magnitude. Both two-dimensional and three-dimensional cases are considered.

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References

  • Bagi K 2003 Statistical analysis of contact force components in random granular assemblies. Granular Matter 5: 45–54

    Article  MATH  Google Scholar 

  • Brockbank R, Huntley J M, Ball R C 1997 Contact force distribution beneath a three-dimensional granular pile. J. de Physique II 7: 1521–1532

    Article  Google Scholar 

  • Chan S H, Ngan A H W 2005 Statistical distribution of contact forces in packings of deformable spheres. Mech. Mater. 37: 493–506

    Article  Google Scholar 

  • Chan S H, Ngan A H W 2006 Statistical distribution of forces in stressed 2-D low-density materials with random microstructures. Mech. Mater. 38: 1199–1212

    Article  Google Scholar 

  • Cover T M, Thomas J A 1991 Elements of information theory. (New York: John Wiley & Sons)

    MATH  Google Scholar 

  • Edwards S F, Grinev D V, Brujic J 2003 Fundamental problems in statistical physics of jammed packings. Physica A—Stat. Mech. and Appl. 330: 61–76

    Article  MATH  MathSciNet  Google Scholar 

  • Erikson J M, Mueggenburg N W, Jaeger H M, Nagel S R 2002 Force distributions in three-dimensional compressible granular packs. Phys. Rev. E 66: Art. No. 040301

  • Goddard J D 2004 On entropy estimates of contact forces in static granular assemblies. Int. J. Solids and Struct. 41: 5851–5861

    Article  MATH  MathSciNet  Google Scholar 

  • Kruyt N P 2003 Contact forces in anisotropic frictional granular materials. Int. J. Solids and Struct. 40: 3537–3556

    Article  MATH  Google Scholar 

  • Kruyt N P, Rothenburg L 2002 Probability density functions of contact forces for cohesionless frictional granular materials. Int. J. Solids and Struct. 39: 571–583

    Article  MATH  Google Scholar 

  • Liu S H 2006 Simulating a direct shear box test by DEM. Can. Geotech. J. 43: 155–168

    Article  Google Scholar 

  • Metzger P T 2004 Granular contact force density of states and entropy in a modified Edwards ensemble. Phys. Rev. E 70: Art. No. 051303

  • Nicot F, Darve F 2005 A multi-scale approach to granular materials. Mech. Mater. 37: 980–1006

    Google Scholar 

  • Ostojic S, Somfai E, Nienhuis B 2006 Scale invariance and universality of force networks in static granular matter. Nature 439: 828–830

    Article  Google Scholar 

  • Prudnikov A P, Brychkov Y A, Marichev O I 1986 Integrals and Series, volume 1. (Amsterdam: Gordon and Breach Science Publishers)

    Google Scholar 

  • Radeke C, Bagi K, Palancz B, Stoyan D 2004 On probability distributions of contact force magnitudes in loaded dense granular media. Granular Matter 6: 17–26

    Article  MATH  Google Scholar 

  • Radeke C, Glaser H, Stoyan D 2002 Force distribution analysis in loaded planar disc systems by means of FEM. Granular Matter 4: 71–76

    Article  MATH  Google Scholar 

  • Radjai F, Roux S, Moreau J J 1999 Contact forces in a granular packing. Chaos 9: 544–550

    Article  MATH  Google Scholar 

  • Sandstrom C R, Tucker C L 1993 A theory for concentrated fibre suspensions with strong fibre-fibre interactions. Makromolekulare Chemie—Macromolecular Symposia 68: 291–300

    Google Scholar 

  • Schollmann S 1999 Simulation of a two-dimensional shear cell. Phys. Rev. E 59: 889–899, Part B

    Article  Google Scholar 

  • Snoeijer J H, Ellenbroek W G, Vlugt T J H, van Hecke M 2006 Sheared force networks: Anisotropies, yielding, and geometry. Phys. Rev. Lett. 96: Art. No. 098001

  • Tighe B P, Socolar J E S, Schaeffer D G, Mitchener W G, Huber M L 2005 Force distributions in a triangular lattice of rigid bars. Phys. Rev. E 72: Art. No. 031306

  • Vargas W L, Murcia J C, Palacio L E, Dominguez D M 2003 Fractional diffusion model for force distribution in static granular media. Phys. Rev. E 68: Art. No. 021302

  • Youngquist R C, Metzger P T, Kilts K N 2005 Force density function relationships in 2-D granular media. SIAM J. Appl. Math. 65: 1855–1869

    Article  MATH  MathSciNet  Google Scholar 

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  1. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    Saralees Nadarajah

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  1. Saralees Nadarajah
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Correspondence to Saralees Nadarajah.

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Nadarajah, S. Some explicit expressions for the probability distribution of force magnitude. Sadhana 33, 357–365 (2008). https://doi.org/10.1007/s12046-008-0024-3

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  • DOI: https://doi.org/10.1007/s12046-008-0024-3

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