The dynamics of unsteady frictional slip pulses.

Self-healing slip pulses are major spatiotemporal failure modes of frictional systems, featuring a characteristic size [Formula: see text] and a propagation velocity [Formula: see text] ([Formula: see text] is time). Here, we develop a theory of slip pulses in realistic rate- and state-dependent frictional systems. We show that slip pulses are intrinsically unsteady objects-in agreement with previous findings-yet their dynamical evolution is closely related to their unstable steady-state counterparts. In particular, we show that each point along the time-independent [Formula: see text] line, obtained from a family of steady-state pulse solutions parameterized by the driving shear stress [Formula: see text], is unstable. Nevertheless, and remarkably, the [Formula: see text] line is a dynamic attractor such that the unsteady dynamics of slip pulses (when they exist)-whether growing ([Formula: see text]) or decaying ([Formula: see text])-reside on the steady-state line. The unsteady dynamics along the line are controlled by a single slow unstable mode. The slow dynamics of growing pulses, manifested by [Formula: see text], explain the existence of sustained pulses, i.e., pulses that propagate many times their characteristic size without appreciably changing their properties. Our theoretical picture of unsteady frictional slip pulses is quantitatively supported by large-scale, dynamic boundary-integral method simulations.

Dynamic Crack-Front Deformations in Cohesive Materials.

Crack fronts deform due to heterogeneities, and inspecting these deformations can reveal local variations of material properties, and help predict out-of-plane damage. Current models neglect the influence of a finite dissipation length scale behind the crack tip, called the process zone size. The latter introduces scale effects in the deformation of the crack front, that are mitigated by the dynamics of the crack. We provide and numerically validate a theoretical framework for dynamic crack-front deformations in heterogeneous cohesive materials, a key step toward identifying the effective properties of a microstructure.

Earthquake Nucleation Along Faults With Heterogeneous Weakening Rate.

The transition from quasistatic slip growth to dynamic rupture propagation constitutes one possible scenario to describe earthquake nucleation. If this transition is rather well understood for homogeneous faults, how the friction properties of multiscale asperities may influence the overall stability of seismogenic faults remains largely unclear. Combining classical nucleation theory and concepts borrowed from condensed matter physics, we propose a comprehensive analytical framework that predicts the influence of heterogeneities of weakening rate on the nucleation length L c for linearly slip-dependent friction laws. Model predictions are compared to nucleation lengths measured from 2D dynamic simulations of earthquake nucleation along heterogeneous faults. Our results show that the interplay between frictional properties and the asperity size gives birth to three instability regimes (local, extremal, and homogenized), each related to different nucleation scenarios, and that the influence of heterogeneities at a scale far lower than the nucleation length can be averaged.