Mechanics of wrinkled graphene membranes

Abstract

The outstanding mechanical properties of graphene have made it a suitable candidate for awide range of sensor and actuator applications in modern technology. However, before the full potential of future applications can be achieved, a proper characterisation of the fundamental properties of graphene is crucial. The aim of this project was to contribute to the understanding of the mechanics of graphene membranes in presence of surface imperfections. To this end two configurations are investigated: ribbons and cantilevers, respectively. Wrinkled graphene nanoribbons are used to investigate the mechanical behaviour during the transition from the wrinkled state to the flat state. A molecular dynamics model has been developed of a single layer graphene ribbon to describe both the formation of wrinkles as well as the transition from the wrinkled state to the flat state. Also, a continuum model was developed to investigate the formation of wrinkles in graphene nanoribbons. Different constitutive laws have been investigated to describe the mechanical response of wrinkled membranes during the transition from the wrinkled state to the flat state. It was concluded that an exponential version of Hooke’s law fails to describe this transition correctly. The transition is however well described by the first order compressible Ogden’s law. Ogden’s law provided further insights into different mechanical properties of the wrinkled layer. Ogden’s law predicted that wrinkledmembranes exhibit a negative Poisson’s ratio at small strains, which is in agreement with previous research. Also, Ogden’s law predicted a decreasing shearmodulus and an increasing Poisson’s ratio after flattening of the membrane. Single layer graphene cantilevers show great potential, however, due to the difficult manufacturing of these fragile structures they remain virtually unstudied. Herein, a molecular dynamics model has been developed to investigate if nanocantilevers could be stabilised by implying a curvature. We found that, depending on the aspect ratio of the membrane and the applied rate of curvature, single layer graphene cantilevers could be (partly) stabilised by implying a curvature. In conclusion, with this research we provided new insights for designing and investigating the next generation of graphene nanoelectromechanical devices.