Residual stress distributions and mechanical noise in athermally deformed amorphous solids from atomistic simulations

The distribution P(x) of local residual stresses in amorphous packings governs the statistical properties of global collective failure events at the yielding transition. We reveal the evolution of P(x) upon deformation by combining atomistic simulations with the frozen matrix approach. A pseudogap form P(x) ~ x^Θ is observed in the freshly quenched state and in the early stages of deformation. After a few percent strain, however, P(x) starts to develop a plateau p₀ in the small x-limit, where p₀ ~ L^-p with L the system size. A direct comparison with the system size scaling of the stress drops shows that the distribution of avalanche sizes are controlled by Θ in the transient regime and the plateau exponent p in the steady state flow. The broad distribution of mechanical noise P(|Δx|) ~ |Δx|^-1-µ is characterized by a Levy-exponent μ and can be related to the behavior of P(x) via a mean-field description.