Encoding, retrieving and erasing mechanical memories in a crumpled sheet

Crumpling a thin sheet endows it with unusual mechanical properties, such as an intermittent mechanical response and slow relaxation under load. One of the most staggering properties of crumpled sheets is their ability to retain memories - e.g., a memory of the largest load they have been subjected to, or the durations of past mechanical perturbations.

We study the behavior of crumpled sheets under cyclic strain. The mechanical response, as measured by stress-strain curves, converges to limit cycles with repetitive discrete stress drops. These, we show, encode a memory of the strain history of the sheet, particularly of the largest applied strain. We investigate how this phenomenon is encoded in the crumpled structure, and find that the stress drops are the result of hysteretic switching of localized degrees of freedom distributed across the sheet. We show that the observed memories emerge from the elastic coupling between these spatially localized hysterons, and demonstrate in numerical simulations that a simple model of coupled bi-stable elements captures many of the observed effects. Our studies reveal a hierarchical structure of internal states with both reversible and irreversible pathways, which we utilize to devise ways for encoding, retrieving and erasing memories.