Extremal Model for Amorphous Media Plasticity

An extremal model for the plasticity of amorphous materials is studied in a simple two-dimensional antiplane geometry. The steady state is analyzed through numerical simulations. Long-range spatial and temporal correlations in local slip events are shown to develop, leading to nontrivial and highly anisotropic scaling laws. In particular, the plastic strain is shown to concentrate statistically over a region which tends to align perpendicular to the displacement gradient. By construction, the model can be seen as giving rise to a depinning transition, the threshold of which (i.e., the macroscopic yield stress) also reveals scaling properties reflecting the localization of the activity.