The mechanics of dynamic shear crack propagation

Abstract

A recent trend in seismology has been to model the earthquake source as a dynamically extending shear crack, and several basic concepts which seem to be important in this modeling process are examined. First, the universal spatial dependence of the plane elastodynamic stress and velocity fields near a sharp propagating crack tip is demonstrated for both subsonic and transsonic crack speeds, and the corresponding energy release rates are considered. Next, a class of steady state shear crack propagation problems is analyzed, based on both a direct stress analysis approach and an energy integral approach which obviates the need for a complete stress analysis in some cases. Several distinct stress differences which correspond to some of the common definitions of stress drop are involved in the analysis of these simple problems. Finally, some analytical considerations are presented which are relevant to rupture velocity determination for transient shear crack growth according to various fracture criteria, such as the critical stress intensity factor criterion, the critical energy release rate criterion, and the critical stress level criterion. Possible effects of spatially nonuniform stress drop and frictional resistance on rupture propagation are also discussed.

Complex networks and waveforms from acoustic emissions in laboratory earthquakes

“…Considering χ < 0 indicates that decreasing < T > results in increasing the rupture velocity (i.e., < T > ∝ χ in parameter space). The obtained result is comparable with the results of several investigations regarding the weak increase of with rupture velocity (Freund, 1979;Livne et al, 2008). Note that this conclusion is based on the assumption of constant stress drop which corresponds to a constant value for Q = Q max − Q min .…”

Influence of the rupture initiation on the intersonic transition: Crack‐like versus pulse‐like modes

“…[3] In the limit of the singular elastodynamics, admissible speeds v for steady-state propagation are shown to exist in both sub-Rayleigh and intersonic domains [Freund, 1979;Broberg, 1999]. While in the sub-Rayleigh range the stress is square-root singular with the energy release rate G decreasing to zero as v !…”

Recent developments in dynamic fracture: some perspectives

“…of frictional rupture fronts and mode II cracks), though, are closely related when the following two conditions are met: (i) The residual stress σ r left behind the rupture front is constant, a situation commonly assumed in the context of earthquake dynamics [142,143,[169][170][171] (ii) The width of the front (the "cohesive zone"), i.e. the length scale over which the residual stress σ r is reached when the front passes a point at the interface, is small compared to other length scales in the system.…”