Spontaneous instabilities and stick-slip motion in a generalized Hebraud-Lequeux model

Abstract

We revisit the Hébraud-Lequeux (HL) model for the rheology of jammed materials and argue that a possibly important time scale is missing from HL's initial specification. We show that our generalization of the HL model undergoes interesting oscillating instabilities for a wide range of parameters, which lead to intermittent, stick-slip flows under constant shear rate. The instability we find is akin to the synchronization transition of coupled elements that arises in many different contexts (neurons, fireflies, financial bankruptcies, etc.). We hope that our scenario could shed light on the commonly observed intermittent, serrated flows of glassy materials under shear.

9 pages, 3 figures

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Cited by in corpus (7)

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• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Aging and linear response in the Hébraud-Lequeux model for amorphous rheology
• Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity
• Ductile and brittle yielding of athermal amorphous solids: a mean-field paradigm beyond the random field Ising model
• Mean field theory of yielding under oscillatory shear