Memory from coupled instabilities in unfolded crumpled sheets

TL;DR

This study investigates how crumpled sheets exhibit memory effects due to geometric instabilities, combining experiments and modeling to understand their complex mechanical behaviors.

Contribution

It introduces a combined experimental and theoretical approach to explain memory formation in crumpled sheets through geometric instabilities.

Findings

Cyclic strain response is intermittent and hysteretic.

Memory of maximum compression is encoded in the sheet.

Multiple memories can be stored after training.

Abstract

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 behaviours lies in understanding the contribution of the complex geometry of the sheet. Here, we combine cyclic driving protocols and 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 behaviours 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.