  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.
