van der Waals adhesion of graphene membranes

We study the nanomechanics of graphene and other ultrathin membranes adhered to substrates with open cavities by van der Waals forces, and subjected to mechanical loads (concentrated or pressure) that cause stretching, decohesion, and/or sliding. We develop analytical models to describe equilibrium configurations similar to those observed in recent nanomechanical experiments, as well as various deformation regimes that occur upon mechanical loading. We apply the analytical models to single layers of graphene and carry out atomistic simulations of graphene adhered to a substrate to validate the models and illustrate the operative phenomena. We obtain excellent agreement between theory and atomistic simulations and identify the influence of van der Waals adhesion energy, membrane elasticity, geometry, and loading on membrane decohesion from and/or sliding along a substrate.