Jump to main content
Jump to site search

Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates


We analyze the behavior of different elastoplastic models approaching the yielding transition. We propose two kind of rules for the local yielding events: yielding occurs above the local threshold either at a constant rate or with a rate that increases as the square root of the stress excess. We establish a family of “static” universal critical exponents which do not depend on this dynamic detail of the model rules: in particular, the exponents for the avalanche size distribution P(S) ∼ SS f(S/Ldf) and the exponents describing the density of sites at the verge of yielding, which we find to be of the form P(x) = P(0) + xθ with P(0) ∼ L-a controlling the extremal statistics. On the other hand, we discuss “dynamical” exponents that are sensitive to the local yielding rule details. We find that, apart form the dynamical exponent z controlling the duration of avalanches, also the flowcurve’s (inverse) Herschel-Bulkley exponent β (γ[γ with combining dot above] ∼ (σ - σc)β) enters in this category, and is seen to differ in ½ between the two yielding rate cases. We give analytical support to this numerical observation by calculating the exponent variation in the Hébraud-Lequeux model and finding an identical shift. We further discuss an alternative mean-field approximation to yielding only based on the so-called Hurst exponent of the accumulated mechanical noise signal, which gives good predictions for the exponents extracted from simulations of fully spatial models.

Back to tab navigation

Publication details

The article was received on 28 May 2019, accepted on 05 Oct 2019 and first published on 07 Oct 2019

Article type: Paper
DOI: 10.1039/C9SM01073D
Soft Matter, 2019, Accepted Manuscript

  •   Request permissions

    Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates

    E. E. Ferrero and E. Jagla, Soft Matter, 2019, Accepted Manuscript , DOI: 10.1039/C9SM01073D

Search articles by author