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Percolating contact subnetworks on the edge of isostaticity

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Abstract

We search for a percolating, strong subnetwork of contacts in a quasi-statically deforming, frictional granular material. Of specific interest in this study is that subnetwork which contributes to the majority of the total deviator stress and is, or is on the edge of being, isostatic. We argue that a subnetwork derived from the minimal spanning trees of a graph—optimized to include as many elastic contacts as possible and which bear normal contact forces above a given threshold delivers such a network. Moreover adding the strong 3-force-cycles to the spanning tree introduces a level of redundancy required to achieve a network that is almost if not isostatic. Results are shown for assemblies of non-uniformly sized circular particles under biaxial compression, in two-dimensions: a discrete element (DEM) simulation of monotonic loading under constant confining pressure, and cyclic loading of photoelastic disks under constant volume.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia

    David M. Walker & Antoinette Tordesillas

  2. School of Chemical Engineering, University of Birmingham, Birmingham, B15 2TT, UK

    Colin Thornton

  3. Department of Physics, Duke University, Box 90305, Durham, NC, 27708, USA

    Robert P. Behringer

  4. CNLS/MPA-CMMS, Los Alamos National Lab, Los Alamos, NM, 87545, USA

    Jie Zhang

  5. US Army Engineer Research & Development Center, Vicksburg, MS, 39180-6199, USA

    John F. Peters

Authors
  1. David M. Walker
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  2. Antoinette Tordesillas
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  3. Colin Thornton
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  4. Robert P. Behringer
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  5. Jie Zhang
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  6. John F. Peters
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Correspondence to Antoinette Tordesillas.

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Walker, D.M., Tordesillas, A., Thornton, C. et al. Percolating contact subnetworks on the edge of isostaticity. Granular Matter 13, 233–240 (2011). https://doi.org/10.1007/s10035-011-0250-y

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