Memory and aging via coupled elastic instabilities in thin crumpled sheets

Crumpling an ordinary thin sheet transforms it into a complex structure with unusual mechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and a range of mechanical memory effects. We describe research focused on understanding these emergent behaviors, reminiscent of those exhibited by glassy systems, and their relation to the geometrical structure of the crumpled sheet.

Using experiments that combine global mechanical measurements, local probing, acoustic measurements, and 3D imaging of crumpled sheets, we build a mesoscopic description of their mechanics. The global measurements reveal memory effects, including hysteresis, memory of the largest strain, and return point memory, as well as clear signatures of underlying intermittent dynamics. Intermittent dynamics are also observed during slow, logarithmic aging of crumpled sheets under load. In this case, however, the intermittent events occur in highly correlated, scale-free avalanches. The complimentary local measurements reveal that the memory and aging behaviors emerge from the collective dynamics of mesoscopic, bistable elements within the sheet: localized geometric instabilities that act as coupled, hysteretic, two-state degrees of freedom.

Based on this picture, we develop a numerical model of a disordered network of bistable elastic elements that corroborates all our findings: hysteresis, intermittencies, memory formation, return point memory, aging, and avalanches. The model highlights the role of interactions and frustration between instabilities in driving these behaviors. The emerging picture is of a disordered system with a complex energy landscape, reminiscent of a mechanical spin-glass, that self-organizes to a state which lies on the verge of instability.