  The onset of frictional motion is mediated by the dynamic propagation of a
rupture front, analogous to a shear crack. The rupture front nucleates
quasi-statically in a localized region of the frictional interface and slowly
increases in size. When it reaches a critical nucleation length it becomes
unstable, propagates dynamically and eventually breaks the entire interface,
leading to macroscopic sliding. The nucleation process is particularly
important because it determines the stress level at which the frictional
interface fails, and therefore, the macroscopic friction strength. However, the
mechanisms governing nucleation of frictional rupture fronts are still not well
understood. Specifically, our knowledge of the nucleation process along a
heterogeneous interface remains incomplete. Here, we study the nucleation of
localized slip patches on linear slip-weakening interfaces with deterministic
and stochastic heterogeneous friction properties. Using numerical simulations,
we analyze the process leading to a slip patch of critical size for systems
with varying correlation lengths of the local friction strength. Our
deterministic interface model reveals that the growth of the critical
nucleation patch at interfaces with small correlation lengths is non smooth due
to the coalescence of neighboring slip patches. Existing analytical solutions
do not account for this effect, which leads to an overestimation of global
interface strength. Conversely, when the correlation length is large, the
growth of the slip patch is continuous and our simulations match the analytical
solution. Furthermore, nucleation by coalescence is also observed on stochastic
interfaces with small correlation length...
