Memory and criticality from coupled instabilities in crumpled sheets

Crumpling an ordinary thin sheet transforms it into a geometrically complex structure with unusual mechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and mechanical memory effects. These emergent behaviors, reminiscent of those exhibited by other nonequilibrium disordered systems, and in particular their relation to the crumpled geometry, remain poorly understood.

I will describe experiments that combine global mechanical measurements, local probing, acoustic measurements and 3D imaging of crumpled sheets to build a mesoscopic description of their mechanics. The results reveal new memory effects as well as critical behaviors, and suggest that these emerge from the collective dynamics of mesoscopic, bistable degrees of freedom within the sheet: localized geometric instabilities that act as coupled mechanical "bits''. Based on this picture, we develop a simple numerical model of coupled bistable elastic elements that corroborates our findings and reveals the role of frustration. The emerging picture is of a system with a complex energy landscape, reminiscent of a mechanical spin-glass.