Unveiling the influence of slip-weakening laws' shapes on rupture dynamics: beyond fracture energy in controlling rupture profiles

Friction plays a crucial role in rupture dynamics and yet its precise nature remains elusive. Consequently, a friction law must be assumed to model rupture. Commonly used constitutive laws for modeling friction include slip-weakening laws which are characterized by a drop from static to dynamic frictional strength. Within this framework, the prevailing understanding asserts that the frictional behaviour is solely controlled by the fracture energy - the area beneath the frictional strength versus the cumulated slip curve. In particular, it is claimed that the curve's shape itself has no influence on the system's response. Here we perform fully dynamic rupture simulations to challenge prevailing beliefs by demonstrating that the constitutive law shape exerts an intimate control over rupture profiles. For a consistent fracture energy but varying constitutive law shapes, the velocity profile is different: each abrupt slope transition leads to the localization of a distinct velocity peak. For example, in the case of a dual slip-weakening law featuring two different slopes, the rupture exhibits two distinct velocity peaks. This distinction significantly influences how a rupture responds to a stress barrier. These results are derived through two separate numerical schemes (spectral boundary integral and finite element methods) ensuring their independence from the computational approach employed.