# Thermal crumpling of perforated two-dimensional sheets

## TL;DR

This study demonstrates that perforating two-dimensional elastic sheets can tune the temperature at which they crumple, with the transition governed by the total removed area rather than hole arrangement.

## Contribution

We introduce a method to control the crumpling transition in elastic membranes by modifying their geometry and topology through perforations.

## Key findings

- Critical temperature depends on total perforated area.
- Critical exponents match standard crumpling transition.
- Perforation arrangement does not affect transition temperature.

## Abstract

Thermalized elastic membranes without distant self-avoidance are believed to undergo a crumpling transition when the microscopic bending stiffness is comparable to $kT$, the scale of thermal fluctuations. Most potential physical realizations of such membranes have a bending stiffness well in excess of experimentally achievable temperatures and are therefore unlikely ever to access the crumpling regime. We propose a mechanism to tune the onset of the crumpling transition by altering the geometry and topology of the sheet itself. We carry out extensive molecular dynamics simulations of perforated sheets with a dense periodic array of holes and observe that the critical temperature is controlled by the total fraction of removed area, independent of the precise arrangement and size of the individual holes. The critical exponents for the perforated membrane are compatible with those of the standard crumpling transition.