Percolating contact subnetworks on the edge of isostaticity

DM Walker, A Tordesillas, Colin Thornton, RP Behringer, J Zhang, JF Peters

Research output: Contribution to journalArticle

14 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)233-240
Number of pages8
JournalGranular Matter
Issue number3
Publication statusPublished - 1 Jun 2011


  • Isostatic
  • Force cycles
  • Force chains
  • Spanning trees
  • Complex networks


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