  Continuum modeling of free-standing graphene monolayer, viewed as a two
dimensional 2-lattice, requires specification of the components of the shift
vector that acts as an auxiliary variable. If only in-plane motions are
considered the energy depends on an in-plane strain measure and the shift
vector. The assumption of geometrical and material linearity leads to quadratic
energy terms with respect to the shift vector, the strain tensor, and their
combinations. Graphene's hexagonal symmetry reduces the number of independent
moduli then to four. We evaluate these four material parameters using molecular
calculations and the AIREBO potential and compare them with standard linear
elastic constitutive modeling. The results of our calculations show that the
predicted values are in reasonable agreement with those obtained solely from
our molecular calculations as well as those from literature. To the best of our
knowledge, this is the first attempt to measure mechanical properties when
graphene is modeled as a hexagonal 2-lattice. This work targets at the
continuum scale when the insight measurements comes from finer scales using
atomistic simulations.
