Depinning in a two-layer model of plastic flow

TL;DR

This paper investigates a two-layer elastic model driven over a random substrate, revealing how viscous coupling influences depinning transitions, hysteresis, and stability across different dimensions through mean-field, RG, and perturbative analyses.

Contribution

It introduces a detailed analysis of viscous coupling effects on depinning and hysteresis in layered elastic systems, including new universality classes and stability conditions.

Findings

Viscous coupling destabilizes elastic depinning fixed point for d <= 4.

Hysteretic plastic depinning occurs below elastic depinning threshold for d<4.

Stable pinned configurations remain stable with viscous coupling in any dimension.

Abstract

We study a model of two layers, each consisting of a d-dimensional elastic object driven over a random substrate, and mutually interacting through a viscous coupling. For this model, the mean-field theory (i.e. a fully connected model) predicts a transition from elastic depinning to hysteretic plastic depinning as disorder or viscous coupling is increased. A functional RG analysis shows that any small inter-layer viscous coupling destablizes the standard (decoupled) elastic depinning FRG fixed point for d <= 4, while for d > 4 most aspects of the mean-field theory are recovered. A one-loop study at non-zero velocity indicates, for d<4, coexistence of a moving state and a pinned state below the elastic depinning threshold, with hysteretic plastic depinning for periodic and non-periodic driven layers. A 2-loop analysis of quasi-statics unveils the possibility of more subtle effects, including a new universality class for non-periodic objects. We also study the model in d=0, i.e. two coupled particles, and show that hysteresis does not always exist as the periodic steady state with coupled layers can be dynamically unstable. It is also proved that stable pinned configurations remain dynamically stable in presence of a viscous coupling in any dimension d. Moreover, the layer model for periodic objects is stable to an infinitesimal commensurate density coupling. Our work shows that a careful study of attractors in phase space and their basin of attraction is necessary to obtain a firm conclusion for dimensions d=1,2,3.