  An existing hyperelastic membrane model for graphene calibrated from
ab-initio data (Kumar and Parks, 2014) is adapted to curvilinear coordinates
and extended to a rotation-free shell formulation based on isogeometric finite
elements. Therefore, the membrane model is extended by a hyperelastic bending
model that reflects the ab-inito data of Kudin et al. (2001). The proposed
formulation can be implemented straight-forwardly into an existing finite
element package, since it does not require the description of molecular
interactions. It thus circumvents the use of interatomic potentials that tend
to be less accurate than ab-initio data. The proposed shell formulation is
verified and analyzed by a set of simple test cases. The results are in
agreement to analytical solutions and satisfy the FE patch test. The
performance of the shell formulation for graphene structures is illustrated by
several numerical examples. The considered examples are indentation and peeling
of graphene and torsion, bending and axial stretch of carbon nanotubes.
Adhesive substrates are modeled by the Lennard-Jones potential and a coarse
grained contact model. In principle, the proposed formulation can be extended
to other 2D materials.
