Depinning in a two-layer model of plastic flow

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 renormalization group analysis shows that any small interlayer viscous coupling destabilizes the standard (decoupled) elastic depinning functional renormalization group fixed point for d≤4, while for d>4 most aspects of the mean-field theory are recovered. A one-loop study at nonzero 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 nonperiodic driven layers. A two-loop analysis of quasistatics unveils the possibility of more subtle effects, including a new universality class for nonperiodic 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.