Avalanche size distributions in mean field plastic yielding models

Abstract

I discuss the size distribution $\mathcal{N}(S)$ of avalanches occurring at the yielding transition of mean field (i.e., Hebraud-Lequeux) models of amorphous solids. The size distribution follows a power law dependence of the form: $\mathcal{N}(S)\sim S^{-\tau }$. However (contrary to what is found in its depinning counterpart) the value of $\tau$ depends on details of the dynamic protocol used. For random triggering of avalanches I recover the $\tau =3/2$ exponent typical of mean field models, which in particular is valid for the depinning case. However, for the physically relevant case of external loading through a quasistatic increase of applied strain, a smaller exponent (close to 1) is obtained. This result is rationalized by mapping the problem to an effective random walk in the presence of a moving absorbing boundary.

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• Elastic interfaces on disordered substrates: From mean-field depinning to yielding
• Yielding transition of a two dimensional glass former under athermal cyclic shear deformation
• Avalanches and Structural Change in Cyclically Sheared Silica Glass
• Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media
• Protocol dependence for avalanches under constant stress in elastoplastic models
• Ductile and brittle yielding of athermal amorphous solids: a mean-field paradigm beyond the random field Ising model
• Thermally activated intermittent flow in amorphous solids
• Dynamic phase diagram of plastically deformed amorphous solids at finite temperature