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An existing hyperelastic membrane model for graphene calibrated fromab-initio data (Kumar and Parks, 2014) is adapted to curvilinear coordinatesand extended to a rotation-free shell formulation based on isogeometric finiteelements. Therefore, the membrane model is extended by a hyperelastic bendingmodel that reflects the ab-inito data of Kudin et al. (2001). The proposedformulation can be implemented straight-forwardly into an existing finiteelement package, since it does not require the description of molecularinteractions. It thus circumvents the use of interatomic potentials that tendto be less accurate than ab-initio data. The proposed shell formulation isverified and analyzed by a set of simple test cases. The results are inagreement to analytical solutions and satisfy the FE patch test. Theperformance of the shell formulation for graphene structures is illustrated byseveral numerical examples. The considered examples are indentation and peelingof graphene and torsion, bending and axial stretch of carbon nanotubes.Adhesive substrates are modeled by the Lennard-Jones potential and a coarsegrained contact model. In principle, the proposed formulation can be extendedto other 2D materials.

A new shell formulation for graphene structures based on existing ab-initio data