Multi-persistence Analysis of Granular Contact Networks Approaching Failure

The network of contact forces in a granular material reveals multiscale heterogeneity and coordination. Motivated by a desire to identify coherent, mechanical structures which produce the emergent bulk mechanical properties of such materials, many researchers have turned to tools from the field of topology. Recently, the persistence of topological features in the contact force network has been shown to strongly correlate to the mechanical response of the material [1-3]. We expand on this technique by studying the multi-parameter persistence of the contact network. We compute persistence for simultaneous filtration of parameters including force magnitude, but also network properties such as centrality or coordination number. We apply this analysis to experimentally measured force networks approaching the threshold for plastic deformation. In preliminary results we find persistent features correlated to material rigidity which single-parameter persistent homology is unable to identify.



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[2] Luding et al., Understanding slow compression…, Soft Matter, 2022, 18, 1868-1884

[3]Dijksman et al., Characterizing granular networks…, Phys. Rev. E, 2018, 97, 042903