  Understanding the interaction mechanics between graphene layers and co-axial
carbon nanotubes (CNTs) is essential for modeling graphene and CNT-based
nanoelectromechanical systems. This work proposes a new continuum contact model
to study interlayer interactions between curved graphene sheets. The continuum
model is calibrated and validated using molecular dynamics (MD) simulations.
These are carried out employing the reactive empirical bond order
(REBO)+Lennard-Jones (LJ) to model the interactions within a sheet, while the
LJ, Kolmogorov-Crespi (KC), and Lebedeva potentials are used to model the
interactions between sheets. The continuum contact model is formulated for
separation distances greater than 0.29nm, when sheet deformations are
sufficiently small and do not affect the sheet interactions substantially. This
allows to treat the master contact surface as rigid, thus simplifying the
contact formulation greatly. The model calibration is conducted systematically
for a sequence of different stackings using existing and newly proposed ansatz
functions. The calibrated continuum model is then implemented in a curvilinear
finite element (FE) shell formulation to investigate the pull-out and twisting
interactions between co-axial CNTs. The resisting pull-out forces and torques
depend strongly on the chirality of the considered CNTs. The absolute
differences between FE and MD results are very small, and can be attributed to
model assumptions and loading conditions.
