Buckling kinetics of graphene membranes under uniaxial compression

Despite past investigations of the buckling instability, the kinetics of the buckling process is not well understood. We develop a generic framework for determining the buckling kinetics of membranes under compressive stress (σ_{b}) via molecular dynamics simulations. The buckling time (t_{b}) is modeled by an extended Boltzmann-Arrhenius-Zhurkov equation accounting for temperature (T) and scale-dependent bending rigidity. We discern three regimes: (I) t_{b} decreases with T; (II) t_{b} increases with T; (III) t_{b} is T independent. Regime II coheres with the predictions of the theory of fluctuating sheets (TFS). Regime I is seen at small scales due to fluctuations about equilibrium and is not predicted by the TFS.