We study theoretically the deposition of few layer graphene sheets onto a grooved substrate incorporating adhesion between substrate and sheet. We develop a model to understand the equilibrium of the sheet allowing for partial conformation of sheet to substrate. This model gives physical insight into recent observations of “snap-through” from flat to conforming states and emphasizes the crucial role of substrate shape in determining the nature of this transition. Our analytical results are consistent with numerical simulations using a van der Waals-like interaction. Finally, we propose a substrate shape that should exhibit a continuous, rather than “snap-through”, transition.

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