Thermal effects and scaling theory for the yielding transition in amorphous solids

The yielding transition in amorphous solids has been thoroughly studied in the athermal-quasistatic (AQS) limit. Finite temperature and driving rate introduce new, competing timescales to the problem that create new scaling behavior. We investigate these effects by adding thermal noise to a mesoscopic elastoplastic model (EPM). By studying low-temperature and low driving, we retain a clear separation of timescales between avalanches and loading. We principally study the distribution of weak sites p(x) and the scaling of the avalanche size distributions p(s) and develop a mean-field scaling theory for these distributions based on a random-walker description. This mean-field theory satisfactorily collapses results from a thermal 2-dimensional elastoplastic model and predicts three distinct finite-scaling regimes: an AQS regime below a critical temperature, a trivial molten state above another critical temperature, and an intermediate regime with non-trivial scaling.  In addition to the scaling theory, we also find the appearance of temperature dependent stress-localization and characterize the resulting stress-overshoot.