Rate-dependent diffusion in a mesoscopic model of amorphous plasticity: the role of viscous drag and disorder

We study the distribution of energy dissipation rates, stress drops and displacements in a mesoscopic, hybrid lattice-particle model of amorphous plasticity. In the model, the plane is tiled up with plaquettes defined by their vertices, which follow an overdamped dynamics. Plasticity is introduced via a continuous strain energy function with subsequent minima. In the lack of disorder, the strain energy function is periodic, whereas in the presence of disorder the distances between the minima are distributed. We show that in the lack of disorder, after finite strain, the system is locked into a homogeneous stress state with system-wide, synchronous bursts. As disorder is gradually introduced, this synchronous state is suppressed and the jerky plastic flow appears. For the latter case, we observe the occurence of slip lines and a corresponding diffusive behavior and we study the rate dependence of the displacement distributions. Finally, we investigate the role of the particular form of the drag by considering either a viscous or a Stokes drag and compare our results to particle simulations.