  The capacity of popular classical interatomic potentials to describe elastic
properties of graphene is tested. The Tersoff potential, Brenner reactive
bond-order potentials REBO-1990, REBO-2000, REBO-2002 and AIREBO as well as
LCBOP, PPBE-G, ReaxFF-CHO and ReaxFF-C2013 are considered. Linear and
non-linear elastic response of graphene under uniaxial stretching is
investigated by static energy calculations. The Young's modulus, Poisson's
ratio and high-order elastic moduli are verified against the reference data
available from experimental measurements and ab initio studies. The density
functional theory calculations are performed to complement the reference data
on the effective Young's modulus and Poisson's ratio at small but finite
elongations. It is observed that for all the potentials considered, the elastic
energy deviates remarkably from the simple quadratic dependence already at
elongations of several percent. Nevertheless, LCBOP provides the results
consistent with the reference data and thus realistically describes in-plane
deformations of graphene. Reasonable agreement is also observed for the
computationally cheap PPBE-G potential. REBO-2000, AIREBO and REBO-2002 give a
strongly non-linear elastic response with a wrong sign of the third-order
elastic modulus and the corresponding results are very far from the reference
data. The ReaxFF potentials drastically overestimate the Poisson's ratio.
Furthermore, ReaxFF-C2013 shows a number of numerical artefacts at finite
elongations. The bending rigidity of graphene is also obtained by static energy
calculations for large-diameter carbon nanotubes. The best agreement with the
experimental and ab initio data in this case is achieved using the REBO-2000,
REBO-2002 and ReaxFF potentials. Therefore, none of the considered potentials
adequately describes both in-plane and out-of-plane deformations of graphene.
