Network configurations of dynamic friction patterns

Department of Civil Engineering and Lassonde Institute, University of Toronto - Toronto, 170 college street, M5S3E3, ON, Canada

^a h.o.ghaffari@gmail.com

Received: 7 February 2012
Accepted: 24 April 2012

Abstract

The complex configurations of dynamic friction patterns, regarding real-time contact areas, are transformed into appropriate networks. In this letter, we analyze the dynamics of static friction, i.e. nucleation processes, with respect to friction networks. We show that networks can successfully capture the crack-like shear ruptures and possible corresponding acoustic features. We found that the fraction of triangles scales remarkably with the detachment fronts. There is a universal power law between nodes’ degrees and motifs’ frequencies (for triangles, it reads T(k)k∝k^β (β ≈ 2 ± 0.4)). In particular, the evolutions of loops are scaled with power law, indicating the aggregation of cycles around hub nodes. Furthermore, the motif distributions and modularity space of networks —in terms of within-module degrees and participation coefficients— show universal trends, indicating a common aspect of energy flow in shear ruptures. Moreover, we confirmed that slow ruptures generally hold small localization, while regular ruptures carry a high level of energy localization. We proposed that assortativity, as an index to correlation of a node's degree, can uncover acoustic features of the interfaces.