On the isotropic elastic properties of graphene crystal lattice

Graphene is a monolayer of carbon atoms packed into a two-dimensional honeycomb lattice. This allotrope can be considered as mother of all graphitic forms of carbon. The elastic in-plane properties of graphene are studied. Nowadays graphene often is simulated as a two-dimensional elastic continuum. It is shown in this work that if this continuum has the same symmetric properties as graphene crystal, then the continuum is isotropic while the small deformations are considered. A simple and mathematically rigorous proof of this statement is given. The proof is based on the orthogonal transformation of the coordinates of the continual stress and strain tensors and comparison of the elastic tensor components before and after transformation