  The onset of frictional motion is mediated by rupture-like slip fronts, which
nucleate locally and propagate eventually along the entire interface causing
global sliding. The static friction coefficient is a macroscopic measure of the
applied force at this particular instant when the frictional interface loses
stability. However, experimental studies are known to present important scatter
in the measurement of static friction; the origin of which remains unexplained.
Here, we study the nucleation of local slip at interfaces with slip-weakening
friction of random strength and analyze the resulting variability in the
measured global strength. Using numerical simulations that solve the
elastodynamic equations, we observe that multiple slip patches nucleate
simultaneously, many of which are stable and grow only slowly, but one reaches
a critical length and starts propagating dynamically. We show that a
theoretical criterion based on a static equilibrium solution predicts
quantitatively well the onset of frictional sliding. We develop a Monte-Carlo
model by adapting the theoretical criterion and pre-computing modal convolution
terms, which enables us to run efficiently a large number of samples and to
study variability in global strength distribution caused by the stochastic
properties of local frictional strength. The results demonstrate that an
increasing spatial correlation length on the interface, representing geometric
imperfections and roughness, causes lower global static friction. Conversely,
smaller correlation length increases the macroscopic strength while its
variability decreases. We further show that randomness in local friction
properties is insufficient for the existence of systematic precursory slip
events. Random or systematic non-uniformity in the driving force, such as
potential energy or stress drop, is required for arrested slip fronts. Our
model and observations...
