Collective and finite-size effects on local yield distributions in mesoscopic models of amorphous plasticity

The distribution of local proximity to yielding, p(x), governs the statistical properties of failure events in the yielding transition of amorphous solids. In the thermodynamic limit, p(x) has a pseudogap of the form p(x)∼x^θ. Using a mesoscopic model of amorphous plasticity under strain-controlled athermal quasistatic loading conditions, we show that for finite-systems p(x) has a previously unrecognized intermediate power-law deviating from the pseudogap exponent θ, before entering a terminal plateau with p(x«1)∼L^-p. We connect these regimes to finite-size effects originating in the mechanical noise and the drift velocity. There is a fundamental difference in the mechanical noise originating from large and small plastic events, and this gives rise to the intermediate power-law regime. We demonstrate that, although the extremal statistic x_min determines the global distance to instability and is located at the entrance to the intermediate power-law, this newly observed regime does not alter established scaling relations between the pseudogap exponent and the yielding exponents.