To model rupture dynamics, a friction law must be assumed. Commonly used constitutive laws include slip- weakening laws which are characterized by a drop from static to dynamic frictional stress over a critical slip distance. Within this framework, the prevailing understanding asserts that the frictional behavior is solely controlled by the fracture energy - the area beneath the frictional stress versus the cumulative 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 dynamics. These results are confirmed using two independent numerical schemes (spectral boundary integral and finite element methods). Fora consistent fracture energy but varying constitutive weakening law shapes, the slip velocity profile is different: each abrupt slope transition leads to the localization of a distinct velocity peak. For example, in the case of a bilinear slip-weakening law featuring two different slopes, the rupture exhibits two distinct velocity peaks. This phenomenon arises from the transition between a constant weakening rate to another. We show that ruptures with the same fracture energy but different constitutive law shapes may respond differently to stress barriers, especially when cumulative slip is below the critical slip D. In these cases, variations ineffective fracture energy across different laws lead to differing outcomes: under one law, a rupture may propagate pasta barrier, while under another, it may arrest. These findings underscore the critical role of constitutive law shape on rupture dynamics, influencing the response to small-scale asperities and heterogeneities and to larger-scale barriers, and highlighting the importance of both fracture energy and weakening mechanisms for seismic hazard assessment.