Graphene is prone to out-of-plane instabilities, with buckling under compression being the most common example. While tensile loading is generally expected to suppress such effects, recent studies on macroscopic elastic sheets have shown that localized tension can induce transverse buckling and giant folding. Whether this mechanism persists in atomically thin materials, however, remains unclear. Here, we demonstrate through molecular-dynamics simulations that when localized tension is applied, graphene develops pronounced out-of-plane folding driven by transverse-compressive stresses. Once folding is initiated, the folding angle follows a robust power-law scaling with the applied strain, enabling quantitative and controllable modulation of the folded morphology. We further demonstrate that the sheet aspect ratio plays a key role in governing the folding response, including the onset of folding and the maximum attainable folding angle. Importantly, this folding behavior and its associated scaling law are found to be robust against moderate thermal fluctuations and low concentrations of lattice defects. These results establish localized tension-induced folding as a robust mechanical instability in graphene and demonstrate that continuum thin-sheet scaling laws remain applicable down to the atomic scale. Our findings provide a framework for tailoring the morphology of graphene and other two-dimensional materials through geometric design and mechanical loading.

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• Buckling
• Mechanical & acoustical properties
• Stress
• Graphene
• Molecular dynamics