Thermally activated flow in models of amorphous solids*

Amorphous solids yield at a critical value Σc of the imposed stress Σ through a dynamical phase transition. While sharp in athermal systems, the presence of thermal fluctuations leads to the rounding of the transition and thermally activated flow even below Σc. Here, we study the steady state thermal flow of amorphous solids using a mesoscopic elasto-plastic model. In the Hébraud-Lequex (HL) model we provide an analytical solution of the thermally activated flow at low temperature. We then propose a general scaling law that also describes the transition rounding. Finally, we find that the scaling law holds in numerical simulations of the HL model, a 2D elasto-plastic model, and in previously published molecular dynamics simulations of 2D Lennard-Jones glass.