Buckling in thin thermalized ribbons under longitudinal compression

Introducing kirigami cuts to thin sheets, ranging from macro to nanoscale, can allow for sensitive control of mechanical properties such as stretchability. The out-of-plane buckling due to in-plane compression can be a key feature in preventing failure upon stretching. While thin plate theory can predict critical buckling for thin frames and nanoribbons at very low temperatures, a unifying framework to describe the effects of thermal fluctuations on the buckling presents subtle problems. In analogy with understanding semi-flexible polymers with long persistence lengths, we address under what conditions a thin thermalized nanoribbon behaves like a classical plate and how its thermal modes compete with the buckling modes. We develop a mean field approach to understand how the critical buckling changes due to thermal fluctuations both above and below the buckling transition. We simulate thin graphene nanoribbons under axial compression using molecular dynamics simulations to test our predictions.