Slow relaxations in disordered mechanical systems - aging on the verge of instability

Slow relaxations are a hallmark of disordered systems trapped in far-from-equilibrium conditions. After a perturbation, many of these systems exhibit logarithmically slow relaxations of one or more of their macroscopic observables. These relaxations can span many time scales, from a fraction of a second to days and even years. However, the microscopic processes underlying this behavior and the reason for its ubiquity across many different systems remain unclear.

Through experiments in crumpled sheets and simulations of a simplified mechanical model, we reveal a general mechanism underlying slow relaxation phenomena. We show that under load, these systems self-organize to a metastable state which is poised on the verge of a local instability, where they can remain for long, but finite times. The system’s relaxation advances via a series of instabilities, each resulting in an avalanche, occurring on short timescales compared to the typical waiting times between instabilities. Crucially, we find that these waiting times increase as the system relaxes, due to the release of internal stress that leads to a slow increase in the effective energy barriers. This, we show, naturally leads to an overall logarithmic relaxation.