Can you hear the shape of a crumpled sheet?

Thin, crumpled sheets show surprisingly intricate dynamics: when subject to a constant load, they exhibit an extremely slow volume relaxation that spans many decades in time – from fractions of a second to weeks. After an abrupt change in the load, they show slow, non-monotonic aging and memory effects reminiscent of glassy systems. We have recently shown that these dynamics and scaling relations can be captured accurately using a phenomenological model in which the relaxation process is assumed to be governed by a linear superposition of many relaxation modes, that have a broad distribution of relaxation times. Here, we study, theoretically and experimentally, the statistics of discrete micro-mechanical relaxation events occurring within the system as it relaxes or exhibits memory. We find that during logarithmic relaxations the waiting time between these micro-mechanical ‘quakes’ displays approximate Poisson-statistics at any point in time, but with an average that grows linearly with the age of the system from preparation. The model is also used to predict the pattern of micro-relaxation events during the non-monotonic aging regime. The model predictions and experimental data of acoustic emission show god agreement.