Elastic instabilities and their frustrated interactions govern the mechanics of thin crumpled sheets

A thin sheet that has been crumpled many times exhibits a range of fascinating mechanical properties, including enhanced rigidity, intermittent response to continuous drives, crackling sounds spanning many scales in intensity, slow relaxations spanning many scales in time, and perhaps most staggeringly, an ability to retain various forms of memory.

We show that these unusual mechanical behaviors, reminiscent of those exhibited by amorphous materials and glassy systems, are the result of the collective dynamics of a large number of mechanical instabilities formed across the sheet during the crumpling process. These localized, bi-stable degrees of freedom interact and frustrate each other, giving rise to complex mechanical responses. Our findings inspire new designs for smart mechanical metamaterials.