Topological Complexity of Frictional Interfaces: Friction Networks

Through research conducted in this study, a network approach to the correlation patterns of void spaces in rough fractures (crack type II) was developed. We characterized friction networks with several networks characteristics. The correlation among network properties with the fracture permeability is the result of friction networks. The revealed hubs in the complex aperture networks confirmed the importance of highly correlated groups to conduct the highlighted features of the dynamical aperture field. We found that there is a universal power law between the nodes' degree and motifs frequency (for triangles it reads T(k)\proptok{\beta} ({\beta} \approx2\pm0.3)). The investigation of localization effects on eigenvectors shows a remarkable difference in parallel and perpendicular aperture patches. Furthermore, we estimate the rate of stored energy in asperities so that we found that the rate of radiated energy is higher in parallel friction networks than it is in transverse directions. The final part of our research highlights 4 point sub-graph distribution and its correlation with fluid flow. For shear rupture, we observed a similar trend in sub-graph distribution, resulting from parallel and transversal aperture profiles (a superfamily phenomenon)

Network-Configurations of Dynamic Friction Patterns

The complex configurations of dynamic friction patterns-regarding real time contact areas- are transformed into appropriate networks. With this transformation of a system to network space, many properties can be inferred about the structure and dynamics of the system. Here, 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 remarkably scales with the detachment fronts. There is a universal power law between nodes' degree and motifs frequency (for triangles, it reads T(k)\proptok{\beta} ({\beta} \approx2\pm0.4)). We confirmed the obtained universality in aperture-based friction networks. Based on the achieved results, we extracted a possible friction law in terms of network parameters and compared it with the rate and state friction laws. In particular, the evolutions of loops are scaled with power law, indicating the aggregation of cycles around hub nodes. Also, the transition to slow rupture is scaled with the fast variation of local heterogeneity. Furthermore, the motif distributions and modularity space of networks -in terms of withinmodule degree and participation coefficient-show non-uniform general trends, indicating a universal aspect of energy flow in shear ruptures

Solitonic State in Microscopic Dynamic Failures

Onset of permanent deformation in crystalline materials under a sharp indenter tip is accompanied by nucleation and propagation of defects. By measuring the spatio-temporal strain field nearthe indenter tip during indentation tests, we demonstrate that the dynamic strain history at the moment of a displacement burst carries characteristics of formation and interaction of local excitations, or solitons. We show that dynamic propagation of multiple solitons is followed by a short time interval where the propagating fronts can accelerate suddenly. As a result of such abrupt local accelerations, duration of the fast-slip phase of a failure event is shortened. Our results show that formation and annihilation of solitons mediate the microscopic fast weakening phase, during which extreme acceleration and collision of solitons lead to non-Newtonian behavior and Lorentz contraction, i.e., shortening of solitons characteristic length. The results open new horizons for understanding dynamic material response during failure and, more generally, complexity of earthquake sources

Complex Networks on a Rock Joint

A complex network approach on a rough fracture is developed. In this manner, some hidden metric spaces (similarity measurements) between apertures profiles are set up and a general evolutionary network in two directions (in parallel and perpendicular to the shear direction) is constructed. Also, an algorithm (COmplex Networks on Apertures: CONA) is proposed in which evolving of a network is accomplished using preferential detachments and attachments of edges (based on a competition and game manner) while the number of nodes is fixed. Also, evolving of clustering coefficients and number of edges display similar patterns as well as are appeared in shear stress, hydraulic conductivity and dilation changes, which can be engaged to estimate shear strength distribution of asperities.Comment: ROCKENG09: Proceedings of the 3rd CANUS Rock Mechanics Symposium, Toronto, May 2009 (Ed: M.Diederichs and G. Grasselli

Functional-Friction Networks: New Insights on the Laboratory Earthquakes

We report some new applications of functional complex networks on acoustic emission waveforms from frictional interfaces. Our results show that laboratory faults undergo a sequence of generic phases as well as strengthening, weakening or fast-slip and slow-slip leading to healing. Also, using functional networks, we extend the dissipated energy due to acoustic emission signals in terms of short-term and long-term features of events. We show that the transition from regular to slow ruptures can have an additional production from the critical rupture class similar to the direct observations of this phenomenon in the transparent samples. Furthermore, we demonstrate detailed sub-micron evolution of the interface due to the short-term evolution of rupture tip, which is represented by phenomenological description of the modularity rates. In addition, we found nucleation phase of each single event for most amplified events follows a nearly constant time scale, corresponding to initial strengthening of interfaces