A state variable for crumpled thin sheets

TL;DR

This paper demonstrates that the complex process of crumpling thin sheets can be effectively described by a single global variable, the total crease length, which captures the dynamics and damage evolution in a deterministic manner.

Contribution

It introduces a simple, global state variable for crumpling dynamics, reducing the complexity of the disordered system to a single measurable quantity.

Findings

Crumpling damage evolution is largely deterministic.

The total crease length depends only on the current state, not history.

This global variable captures the entire crumpling process.

Abstract

Despite the apparent ease with which a sheet of paper is crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity. This complexity arises from the infinite number of configurations a disordered crumpled sheet can take. Here we experimentally show that key aspects of crumpling have a very simple description; the evolution of the damage in crumpling dynamics can largely be described by a single global quantity, the total length of all creases. We follow the evolution of the damage network in repetitively crumpled elastoplastic sheets, and show that the dynamics of this quantity are deterministic, and depend only on the instantaneous state of the crease network and not at all on the crumpling history. We also show that this global quantity captures the crumpling dynamics of a sheet crumpled for the first time. This leads to a remarkable reduction in complexity, allowing a description of a highly disordered system by a single state parameter. Similar strategies may also be useful in analyzing other systems that evolve under geometric and mechanical constraints, from faulting of tectonic plates to the evolution of proteins.