  We deduce a non-linear continuum model of graphene for the case of finite
out-of-plane displacements and small in-plane deformations. On assuming that
the lattice interactions are governed by the Brenner's REBO potential of 2nd
generation and that self-stress is present, we introduce discrete strain
measures accounting for up-to-the-third neighbor interactions. The continuum
limit turns out to depend on an average (macroscopic) displacement field and a
relative shift displacement of the two Bravais lattices that give rise to the
hexagonal periodicity. On minimizing the energy with respect to the shift
variable, we formally determine a continuum model of F\"oppl-von K\'arm\'a
type, whose constitutive coefficients are given in terms of the atomistic
interactions.
