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We study theoretically the deposition of Few Layer Graphene sheets onto agrooved substrate incorporating adhesion between substrate and sheet. Wedevelop a model to understand the equilibrium of the sheet allowing for partialconformation of sheet to substrate. This model gives new insight into recentobservations of 'snap-through' from flat to conforming states and emphasizesthe crucial role of substrate shape in determining the nature of thistransition. Our analytical results are consistent with numerical simulationsusing a van der Waals-like interaction . Finally we propose a novel substrateshape that should exhibit a continuous, rather than 'snap-through', transition.

The sensitivity of Graphene 'Snap-through' to substrate geometry