Memory from coupled instabilities in unfolded crumpled sheets

Dor Shohat, Daniel Hexner, Yoav Lahini

Research output: Contribution to journalArticlepeer-review


Crumpling an ordinary thin sheet transforms it into a structure with unusual mechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and memory retention. A central challenge in explaining these behaviors lies in understanding the contribution of the complex geometry of the sheet. Here we combine cyclic driving protocols and three-dimensional (3D) imaging to correlate the global mechanical response and the underlying geometric transformations in unfolded crumpled sheets. We find that their response to cyclic strain is intermittent, hysteretic, and encodes a memory of the largest applied compression. Using 3D imaging we show that these behaviors emerge due to an interplay between localized and interacting geometric instabilities in the sheet. A simple model confirms that these minimal ingredients are sufficient to explain the observed behaviors. Finally, we show that after training, multiple memories can be encoded, a phenomenon known as return point memory. Our study lays the foundation for understanding the complex mechanics of crumpled sheets and presents an experimental and theoretical framework for the study of memory formation in systems of interacting instabilities.

Original languageEnglish
Article numbere2200028119
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number28
StatePublished - 12 Jul 2022


  • buckling instability
  • crumpling
  • mechanical metamaterials
  • memory


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