Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior

TL;DR

This paper investigates how stress overshoots in an elastic manifold affect depinning transitions, revealing that despite hysteresis and altered avalanche spectra, the critical behavior remains in the same universality class as the dissipative case.

Contribution

It introduces a model incorporating stress overshoots and demonstrates that the critical depinning behavior is unchanged, despite hysteresis and different avalanche dynamics.

Findings

Stress overshoots lower the critical depinning force.

Hysteresis loops vanish in large samples, aligning with dissipative universality.

Avalanche size distribution differs from the dissipative limit during slow force increase.

Abstract

A model of an elastic manifold driven through a random medium by an applied force F is studied focussing on the effects of inertia and elastic waves, in particular {\it stress overshoots} in which motion of one segment of the manifold causes a temporary stress on its neighboring segments in addition to the static stress. Such stress overshoots decrease the critical force for depinning and make the depinning transition hysteretic. We find that the steady state velocity of the moving phase is nevertheless history independent and the critical behavior as the force is decreased is in the same universality class as in the absence of stress overshoots: the dissipative limit which has been studied analytically. To reach this conclusion, finite-size scaling analyses of a variety of quantities have been supplemented by heuristic arguments. If the force is increased slowly from zero, the spectrum of avalanche sizes that occurs appears to be quite different from the dissipative limit. After stopping from the moving phase, the restarting involves both fractal and bubble-like nucleation. Hysteresis loops can be understood in terms of a depletion layer caused by the stress overshoots, but surprisingly, in the limit of very large samples the hysteresis loops vanish. We argue that, although there can be striking differences over a wide range of length scales, the universality class governing this pseudohysteresis is again that of the dissipative limit. Consequences of this picture for the statistics and dynamics of earthquakes on geological faults are briefly discussed.