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Graphene, the 2D form of carbon, has excellent mechanical, electrical andthermal properties and a variety of potential applications including NEMS,protective coatings, transparent electrodes in display devices and biologicalapplications. Adhesion plays a key role in many of these applications. Inaddition, it has been proposed that the electronic properties of graphene canbe affected by elastic deformation caused by adhesion of graphene to itssubstrate. In light of this, we present here a continuum mechanics basedtheoretical framework to understand the effect of nanoscale morphology ofsubstrates on adhesion and mechanics of graphene. In the first part, we analyzethe adhesion mechanics of graphene on 1 and 2D periodic corrugations. Wecarried out molecular statics simulations and found the results to be in goodagreement with our theory. We modeled adhesive interactions surface forcesdescribed by Lennard-Jones 6-12 potential in both our analysis and simulationsand in principle can be extended to any other interaction potential. Theresults show that graphene adheres conformally to substrates with largecurvatures. We showed in principal that the theory developed here can beextended to substrates of arbitrary shapes that can be represented by a Fourierseries. In the second part, we study the mechanics of peeling of grapheneribbons from 1D sinusoidally textured substrates. In the molecular staticssimulations, we observed two key features in the peel mechanics of the ribbons:the ribbons slide over the substrate and undergo adhesion and peeling near thecrack front in an oscillatory manner, the frequency of which reveals thewavelength of the underlying substrate. Our theory qualitatively captures thesefeatures of the peel mechanics and is general enough that it can be extended toother 2D materials like MoS2, BN etc and different kinds of interactionpotentials.

Adhesion mechanics of graphene on textured substrates