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On probability distributions of contact force magnitudes in loaded dense granular media

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Abstract

This paper discusses possible models for probability distributions of contact force magnitudes in loaded granular media. Many authors have studied such distributions, based on experiments with real particles as well as simulations in 2D and 3D. This has led to various and partly contradicting suggestions for the form of those distributions, which are described in the present paper. Its new theoretical investigations start from the empirically justified assumption that the components of contact forces follow exponential distributions with a certain dependence structure. This leads to distributions of force magnitudes similar to Gamma distributions with shape parameters depending on space dimension, which is in good agreement to results from experiments and numerical simulations. Also the analytical and statistical difficulties of the problem of determination of distributions of force magnitudes are discussed.

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Authors and Affiliations

  1. Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Germany

    Charles Radeke

  2. Hungarian Academy of Science Research Group for Computational Structural Mechanics, Budapest University of Technology and Economics

    Katalin Bagi

  3. Department of Geoinformatics, Budapest University of Technology and Economics

    Béla Paláncz

  4. Institute of Stochastics, TU Bergakademie Freiberg, Germany

    Dietrich Stoyan

Authors
  1. Charles Radeke
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  2. Katalin Bagi
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  3. Béla Paláncz
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  4. Dietrich Stoyan
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Corresponding author

Correspondence to Charles Radeke.

Additional information

In a discussion of Stefan Luding and D.S. the idea arose to consider dependent force components. Niels Kruyt supported our work by sending his papers and by patient discussions via e-mail and a careful reading of an earlier version of this paper.

We had a very useful discussion with Farhang Radjai about the problem P(0)=0 and experiments with real disks. Finally, we are grateful to Tomaso Aste for leading our attention to infinitely divisible distributions.

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Radeke, C., Bagi, K., Paláncz, B. et al. On probability distributions of contact force magnitudes in loaded dense granular media. GM 6, 17–26 (2004). https://doi.org/10.1007/s10035-004-0154-1

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  • DOI: https://doi.org/10.1007/s10035-004-0154-1

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