  Many amorphous glassy materials exhibit complex spatio-temporal mechanical response and rheology, characterized by an intermittent stress-strain response and a fluctuating velocity profile. Under quasistatic and athermal deformation protocols this heterogeneous plastic flow was shown to be composed of plastic events of various sizes. In this paper, through numerical study of a 2D LJ amorphous solid, we generalize the study of the heterogeneous dynamics of glassy materials to the finite shear-rate and temperature case. The global mechanical response obtained through the use of Molecular Dynamics is shown to converge to the quasistatic limit obtained with an energy minimization protocol. The detailed analysis of the plastic deformation at different shear rates shows that the glass follows different flow regimes. At sufficiently low shear rates the mechanical response reaches a shear-rate independent regime that exhibits all the characteristics of the quasistatic response (finite size effects, yield stress...). At intermediate shear rates the rheological properties are determined by the externally applied shear-rate. Finally at higher shear the system reaches a shear-rate independent homogeneous regime. The existence of these three regimes is also confirmed by the detailed analysis of the atomic motion. The computation of the four-point correlation function shows that the transition from the shear-rate dominated to the quasistatic regime is accompanied by the growth of a dynamical cooperativity length scale $\xi$ that is shown to diverge with shear rate. This divergence is compared with the prediction of a simple model that assumes the diffusive propagation of plastic events. 
Plasticity and dynamical heterogeneity in driven glassy materials