Thermally activated flow in models of amorphous solids

Amorphous solids yield at a critical value Σ_c 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 Σ_c. Here we study the steady-state thermal flow of amorphous solids using a mesoscopic elastoplastic 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 two-dimensional (2D) elastoplastic model, and previously published molecular dynamics simulations of 2D Lennard-Jones glass.