Journal article

Percolating contact subnetworks on the edge of isostaticity

David M Walker, Antoinette Tordesillas, Colin Thornton, Robert P Behringer, Jie Zhang, John F Peters



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 assemblie..

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Awarded by US Army Research Office

Awarded by Australian Research Council

Awarded by US NSF

Funding Acknowledgements

We thank Fernando Alonso-Marroquin and our reviewers for their insightful comments and assistance which have significantly improved the paper. This study was supported by the US Army Research Office (W911NF-07-1-0131 for RPB, W911NF-07-1-0370 for AT) and the Australian Research Council (DP0986876 and DP0772409 for AT) and the US NSF (DMR0906908 for RPB).