An overview of universal avalanche statistics at the yielding transition of amorphous solids

In the last years, several groups have described the yielding phenomenon in the deformation of amorphous materials from a statistical physics point of view. To that end, coarse-grained approaches to amorphous solids were introduced, the so-called elasto-plastic models (EPM) [1].
In this talk, I will focus on the statistics of avalanches produced by the characteristic stick-slip behavior close to the yielding transition, enquiring into its common properties among different EPM proposals. I will present in particular the less studied case of EPMs with stress-dependent transition rates for local yielding [2], which help us to see how "dynamical" exponents -those related to the driving speed- may depend on the model details while universality stands more robust for "static" critical exponents.
On the way, the current understanding of yielding from mean-field descriptions and comparison with the depinning transition of a driven elastic line in random media, will be briefly discussed. If time permits, I will further comment on the the strain-rate dependence [3] and inertial effects [4] on the statistics of avalanches as we depart, respectively, from the usually addressed quasistatic and overdamped limits.
 
References:
 
[1] Deformation and flow of amorphous solids: a review of mesoscale elastoplastic models
A. Nicolas, E.E. Ferrero, K. Martens, J.-L. Barrat
Rev. Mod. Phys. 90, 045006 (2018)
 
[2] Static and dynamic critical exponents for elastoplastic models of amorphous solids
E.E. Ferrero and E.A. Jagla, (unpublished).
 
[3] Driving Rate Dependence of Avalanche Statistics and Shapes at the Yielding Transition
C. Liu, E.E. Ferrero, F. Puosi, J.-L. Barrat, and K. Martens
Phys. Rev. Lett. 116, 065501 (2016)
 
[4] Inertia and universality of avalanche statistics: The case of slowly deformed amorphous solids
K. Karimi, E.E. Ferrero, J.-L. Barrat
Phys. Rev. E 95, 013003 (2017)