Mechanical noise dependent aging and shear banding behavior of a mesoscopic model of amorphous plasticity

We discuss aging and localization in a simple ``Eshelby'' mesoscopic model of amorphous plasticity. 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. Mimicking the effect of aging, we focus on the behavior of the model when the initial state is characterized by a distribution of high local yield stress values. A dramatic effect on the localization behavior is obtained: the system first spontaneously self-traps to form a shear band, which then only slowly broadens. The higher the ``age'' parameter the more localized the plastic strain field. Two-time correlations computed on the stress field show a divergent correlation time with the age parameter. The amplitude of a local slip event (the prefactor of the Eshelby singularity) as compared to the yield stress distribution width acts here as a mechanical effective temperaturelike parameter: the lower the slip increment, the higher the localization and the decorrelation time.