Unconventional singularities, scale separation and energy balance in frictional rupture

TL;DR

This paper develops a macroscopic theory showing that frictional rupture deviates from classical crack singularities due to rate-dependent friction, leading to non-edge-localized dissipation and breakdown of scale separation, with implications for earthquake physics.

Contribution

It introduces a theory linking rate-dependent friction to deviations from classical crack singularities and reveals the emergence of non-edge-localized dissipation in frictional rupture.

Findings

Deviations from the square root singularity occur due to rate-dependent friction.

Significant non-edge-localized dissipation emerges even with small deviations.

Predicted dissipation is position-dependent and supported by numerical results.

Abstract

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.