Avalanche statistics at the yielding transition of amorphous solids: universality in elastoplastic models

I focus on the statistics of avalanches produced by the characteristic stick-slip behavior close to the yielding transition in the deformation of amorphous materials, enquiring into its common properties among different elasto-plastic models (EPMs) [1].

I introduce the case of EPMs with stress-dependent transition rates for local yielding [2], showing that "dynamical" exponents might depend on the model details while universality stands robust for "static" critical exponents; in particular, for the exponents for the avalanche size distribution P(S)∼S^−τ_S f(S/L^d_f) and the those describing the density of sites at the verge of yielding, which is found to be of the form P(x)≈P(0)+x^θ with P(0)∼L^−dΦ controlling the extremal statistics [3]. The flowcurve's (inverse) Herschel-Bulkley exponent β is seen to differ in 1/2 between the two yielding rate cases. We further discuss an alternative mean-field approximation to yielding only based on the so-called Hurst exponent of the accumulated mechanical noise signal [2-4]. On the way, the current understanding of yielding in comparison with the depinning transition of a driven elastic line in random media, will be briefly discussed [4].

[1] RMP 90, 045006 (2018)
[2] Soft Matter 15, 9041 (2019)
[3] arXiv:2009.08519 (2020)
[4] PRL 123, 218002 (2019)