  We introduce a torsional force field for sp$^2$ carbon to augment an in-plane
atomistic potential of a previous work (Kalosakas et al, J. Appl. Phys. {\bf
113}, 134307 (2013)) so that it is applicable to out-of-plane deformations of
graphene and related carbon materials. The introduced force field is fit to
reproduce DFT calculation data of appropriately chosen structures. The aim is
to create a force field that is as simple as possible so it can be efficient
for large scale atomistic simulations of various sp$^2$ carbon structures
without significant loss of accuracy. We show that the complete proposed
potential reproduces characteristic properties of fullerenes and carbon
nanotubes. In addition, it reproduces very accurately the out-of-plane ZA and
ZO modes of graphene's phonon dispersion as well as all phonons with
frequencies up to 1000~cm$^{-1}$.
