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 $\left({\sigma }_{\mathrm{b}}\right)$ via molecular dynamics simulations. The buckling time $\left(t_{\mathrm{b}}\right)$ is modeled by an extended Boltzmann-Arrhenius-Zhurkov equation accounting for temperature $\left(T\right)$ and scale-dependent bending rigidity. We discern three regimes: (I) $t_{\mathrm{b}}$ decreases with $T$; (II) $t_{\mathrm{b}}$ increases with $T$; (III) $t_{\mathrm{b}}$ 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.

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• Buckling
• Graphene