  We lay down a nonlinear elastic constitutive framework for the modeling of
some 2D crystals of current interest. The 2D crystals we treat are graphene,
hexagonal boron nitride and some metal dichalcogenides: molybdenium disulfide
(MoS$_2$), tungsten selenium (WSe$_2$), and niobium diselenide (NbSe$_2$). We
first find their arithmetic symmetries by using the theory of monoatomic and
diatomic 2-nets. Then, by confinement to weak transformation neighbourhoods and
by applying the Cauchy-Born rule we are able to use the symmetries continuum
mechanics utilizes: geometric symmetries. We give the complete and irreducible
representation for energies depending on an in-plane measure, the curvature
tensor and the shift vector. This is done for the symmetry hierarchies that
describe how symmetry changes at the continuum level: $\mathcal C_{6 \nu}
\rightarrow \mathcal C_{2 \nu} \rightarrow \mathcal C_1$ for monoatomic 2-nets
and $\mathcal C_{6 \nu} \rightarrow \mathcal C_{1 \nu} \rightarrow \mathcal
C_1$ for diatomic two nets. Having these energies at hand we are able to
evaluate stresses and couple stresses for each symmetry regime.
