Thermalized buckling of isotropically compressed thin sheets

TL;DR

This paper explores how thermal fluctuations and boundary conditions influence buckling in ultrathin elastic sheets, revealing new universality classes and a phase transition behavior with size-dependent critical points.

Contribution

It introduces a comprehensive scaling theory of thermalized buckling, identifying two universality classes and the effects of boundary conditions on critical behavior.

Findings

Boundary conditions induce long-range nonlinear interactions.

Thermal tension leads to renormalization group flow.

Buckling exhibits size-dependent critical points.

Abstract

The buckling of thin elastic sheets is a classic mechanical instability that occurs over a wide range of scales. In the extreme limit of atomically thin membranes like graphene, thermal fluctuations can dramatically modify such mechanical instabilities. We investigate here the delicate interplay of boundary conditions, nonlinear mechanics and thermal fluctuations in controlling buckling of confined thin sheets under isotropic compression. We identify two inequivalent mechanical ensembles based on the boundaries at constant strain (isometric) or at constant stress (isotensional) conditions.Remarkably, in the isometric ensemble, boundary conditions induce a novel long-ranged nonlinear interaction between the local tilt of the surface at distant points. This interaction combined with a spontaneously generated thermal tension leads to a renormalization group description of two distinct universality classes for thermalized buckling, realizing a mechanical variant of Fisher-renormalized critical exponents. We formulate a complete scaling theory of buckling as an unusual phase transition with a size dependent critical point, and discuss experimental ramifications for the mechanical manipulation of ultrathin nanomaterials.