Unconventional singularities and energy balance in frictional rupture

A widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. A distinct feature of ordinary cracks is that their near edge fields are characterized by a square root singularity, which is intimately related to the existence of strict dissipation-related lengthscale separation and edge-localized energy balance. Yet, the interrelations between the singularity order, lengthscale separation and edge-localized energy balance in frictional rupture are not fully understood, even in physical situations in which the conventional square root singularity remains approximately valid. Here we develop a macroscopic theory that shows that the generic rate-dependent nature of friction leads to deviations from the conventional singularity, and that even if this deviation is small, significant non-edge-localized rupture-related dissipation emerges. The physical origin of the latter, which is predicted to vanish identically in the crack analogy, is the breakdown of scale separation that leads an accumulated spatially-extended dissipation, involving macroscopic scales. The non-edge-localized rupture-related dissipation is also predicted to be position dependent. The theoretical predictions are quantitatively supported by available numerical results, and their possible implications for earthquake physics are discussed. Ordinary cracks in bulk materials feature square root singular deformation fields near their edge. Here, the authors show that rupture fronts propagating along frictional interfaces, while resembling ordinary cracks in some respects, feature edge sigularity that differs from the conventional square root one.

Automated summary

The study developed a macroscopic theory showing that the generic rate-dependent nature of friction leads to deviations from the conventional singularity, resulting in significant non-edge-localized rupture-related dissipation. The breakdown of scale separation in fracture leads to accumulated spatially-extended dissipation involving macroscopic scales.