Plastic Response of a 2D Amorphous Solid to Quasi-Static Shear : II - Dynamical Noise and Avalanches in a Mean Field Model

We build a minimal, mean-field, model of plasticity of amorphous solids, based upon a phenomenology of dissipative events derived, in a preceding paper [A. Lemaitre, C. Caroli, arXiv:0705.0823] from extensive molecular simulations. It reduces to the dynamics of an ensemble of identical shear transformation zones interacting via the dynamic noise due to the long ranged elastic fields induced by zone flips themselves. We find that these ingredients are sufficient to generate flip avalanches with a power-law scaling with system size, analogous to that observed in molecular simulations. We further show that the scaling properties of avalanches sensitively depend on the detailed shape of the noise spectrum. This points out the importance of developing a realistic coarse-grained description of elasticity in these systems