Snap-through of graphene nanowrinkles under out-of-plane compression

Nanowrinkles (i.e. the buckled nanoribbons) are widely observed in nano-devices assembled by two-dimensional (2D) materials. The existence of nanowrinkles significantly affects the physical (such as mechanical, electrical and thermal) properties of 2D materials, and thus further, impedes the applications of those devices. In this paper, we take the nanowrinkle formed in a monolayer graphene as a model system to study its deformation behaviours, especially the configuration evolution and the snap-through buckling instabilities, when subjected to the out-of-plane compression. By performing molecular dynamics simulation, the graphene nanowrinkles with or without self-adhesion (which are notated as 'clipped' state or 'bump' state, respectively) are obtained depending on the geometric size and the applied axial compressive pre-strain. The elastica theory is employed to quantify the shape of 'bump' nanowrinkles, as well as the critical condition of the transition between 'clipped' and 'bump' states. By applying out-of-plane compression to the generated graphene nanowrinkle, it flips to an opposite configuration via snap-through buckling. We identify four different buckling modes according to the configuration evolution. An unified phase diagram is constructed to describe those buckling modes. For the cases with negligible van der Waals interaction getting involved in the snap-buckling process, i.e. without self-adhesion, the force-displacement curves for nanowrinkles with same axial pre-strain but different sizes can be scaled to collapse. Moreover, the critical buckling loads can also be scaled and predicted by the extended elastica theory. Otherwise, for the cases with self-adhesion, which corresponds to the greater axial pre-strain, the van der Waals interaction makes the scaling collapse break down. It is expected that the analysis about the snap-through buckling of graphene nanowrinkles reported in this work will advance the understanding of the mechanical behaviours of wrinkled 2D materials and promote the design of functional nanodevices, such as nanomechanical resonators and capacitors.