Mechanical versus thermal activation in driven amorphous solids

Amorphous solids are a disparate class of materials that includes glasses, foams, emulsions, and granular packings. Surprisingly, they exhibit common behaviour in their mechanical response to loading, with an initially elastic regime giving way to a jerky flowing state characterized by intermittent bursts of activity dubbed ``avalanches’’. In the athermal and quasistatic (AQS) limit of slow driving and zero temperature, this steady-state shows the hallmarks of a dynamical phase transition, with power-law scaling for avalanche size and duration, anomalous stress flucutations, and rheological behaviour characterized by nontrivial critical exponents.

Mesoscopic elastoplastic models are ideally suited to reveal universal aspects of this fascinating behavior. In the first part of the talk, we explore how the spatial extent of plastic events affects the distribution of residual stresses, i.e. how far the system is from instability. A key result is the link between the statistical properties of the weakest sites, and the mean stress release caused by collective rearrangements called avalanches [1].

In the second part, we will discuss how finite temperature, driving rate, and finite-size effects compete to truncate avalanches and tune the system away from criticality. Using various scaling arguments and simulations of a mesoscale lattice model of amorphous plasticity equipped with a temperature dependent activation of weak sites, we derive a nonequilibrium phase diagram that captures the onset of avalanche overlap, when temperature effects are prevalent, and when finite-size effects dominate for the critical behaviour [2]. We obtain the macroscopic rheology of sheared amorphous solids with the full mesoscale model as well as a mean-field approximation, and interpret trends with temperature and shear rate in terms of the proposed dynamical phases.