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.

广泛的理解摩擦破裂的框架，例如沿着地质断层的地震，可以与普通的裂缝进行类比。普通裂纹的一个显着特征是其近边缘场的特征是平方根奇异性，这与存在严格的耗散相关的长度尺度分离和边缘局部的能量平衡密切相关。然而，即使在传统的平方根奇异点仍然近似有效的物理情况下，也无法完全理解摩擦断裂中的奇点阶数，长度尺度分离和边缘局部能量平衡之间的相互关系。在这里，我们发展了一种宏观理论，表明摩擦的一般速率相关性会导致与常规奇异性的偏差，即使该偏差很小，出现了与边缘无关的大量与破裂有关的耗散现象。后者的物理起源（在裂纹模拟中被预测会消失相同）是水垢分离的破坏，这导致累积的空间扩展耗散，涉及宏观尺度。非边缘局部破裂相关的耗散也被预测为与位置有关。理论预测得到了可用数值结果的定量支持，并讨论了它们对地震物理学的潜在影响。非边缘局部破裂相关的耗散也被预测为与位置有关。理论预测得到了可用数值结果的定量支持，并讨论了它们对地震物理学的潜在影响。还预测了非边缘局限性破裂相关的耗散与位置有关。理论预测得到了可用数值结果的定量支持，并讨论了它们对地震物理学的潜在影响。