Tuning the mechanical properties and crumpling temperature of thermalised elastic sheets with perforations

Thermalised elastic membranes without distant self-avoidance are believed to undergo a crumpling transition when the microscopic bending stiffness is comparable to kT. 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 crumpling transition by altering the membrane's geometry and topology. We have carried out extensive MD simulations of perforated sheets with a dense array of holes and observed 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. We also explore crumpling in the polymer-like limit of a thin frame and make experimentally relevant predictions for graphene sheets.

[1] D. Yllanes, S. Bhabesh, D.R. Nelson, M.J. Bowick arXiv:1705.07379. Nat. Comm (in press) 2017. DOI: 10.1038/s41467-017-01551-y