Network Theory, Cracking and Frictional Sliding

Abstract: We have developed different network approaches to complex patterns of frictional interfaces (contact areas developments). Here, we analyze the dynamics of static friction. We found, under the correlation measure, the fraction of triangles correlates with the detachment fronts. Also, for all types of the loops (such as triangles), there is a universal power law between nodes' degree and motifs where motifs frequency follow a power law. This shows high energy localization is characterized by fast variation of the loops fraction. Also, this proves that the congestion of loops occurs around hubs. Furthermore, the motif distributions and modularity space of networks -in terms of within-module degree and participation coefficient- show universal trends, indicating an in 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 node's degree, can uncover acoustic features of the interfaces. We showed that increasing assortativity induces a nearly silent period of fault's activities. Also, we proposed that slow ruptures resulted from within-module developments rather than extra-modules of the networks. Our approach presents a completely new perspective of the evolution of shear ruptures.