  We develop a hyperelastic constitutive model for graphene --- describing
in-plane deformations involving both large isotropic and deviatoric strains ---
based on the invariant-theoretic approach to representation of anisotropic
functions. The strain energy density function $\psi$ is expressed in terms of
special scalar-valued functions of the 2D logarithmic strain tensor $ \mathbf
E^{(0)}$ --- called the symmetry-invariants --- that remain invariant w.r.t.
the material symmetry group of graphene, $\mathcal G = \mathcal C_{6v}$. Our
constitutive model conforms to a larger set of \textit{ab initio}
energies/stresses while introducing fewer elastic constants than
previously-proposed models. In particular, when the strain energy is expressed
in terms of symmetry invariants, the material symmetry group is intrinsically
incorporated within the constitutive response functions; consequently, the
elastic constants (of all orders) in the formulation are \textit{a priori}
independent: i.e., no two or more elastic constants are related by symmetry.
This offers substantial simplification in terms of formulation as it eliminates
the need for identifying the independent elastic constants, a task which can
become particularly cumbersome as higher-order terms in the strain energy
density function are incorporated. We validate our constitutive model by
computing (1) the stress and (2) the elastic stability limit for a set of
homogeneous finite deformations --- comprising uniaxial stretch/stress along
the armchair, and the zigzag directions; and equi-biaxial tension. The stress
values predicted by the model are in good agreement with the
directly-calculated \textit{ab initio} values. The elastic stability limits
predicted by acoustic tensor analysis compare well with the predictions from
phonon calculations carried out independently using linear response density
functional perturbation theory.
