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Thermalized elastic membranes without distant self-avoidance are believed toundergo a crumpling transition when the microscopic bending stiffness iscomparable to $kT$, the scale of thermal fluctuations. Most potential physicalrealizations of such membranes have a bending stiffness well in excess ofexperimentally achievable temperatures and are therefore unlikely ever toaccess the crumpling regime. We propose a mechanism to tune the onset of thecrumpling transition by altering the geometry and topology of the sheet itself.We carry out extensive molecular dynamics simulations of perforated sheets witha dense periodic array of holes and observe that the critical temperature iscontrolled by the total fraction of removed area, independent of the precisearrangement and size of the individual holes. The critical exponents for theperforated membrane are compatible with those of the standard crumplingtransition.

Thermal crumpling of perforated two-dimensional sheets