  A mesoscopic model for shear plasticity of amorphous materials in two
dimensions is introduced, and studied through numerical simulations in order to
elucidate the macroscopic (large scale) mechanical behavior. Plastic
deformation is assumed to occur through a series of local reorganizations.
Using a discretization of the mechanical fields on a discrete lattice, local
reorganizations are modeled as local slip events. Local yield stresses are
randomly distributed in space and invariant in time. Each plastic slip event
induces a long-ranged elastic stress redistribution. Rate and thermal effects
are not discussed in the present study. Extremal dynamics allows for recovering
many of the complex features of amorphous plasticity observed experimentally
and in numerical atomistic simulations in the quasi-static regime. In
particular, a quantitative picture of localization, and of the anisotropic
strain correlation both in the initial transient regime, and in the steady
state are provided. In addition, the preparation of the amorphous sample is
shown to have a crucial effect of on the localization behavior.
