Phonon softening and failure of graphene under tensile strain

Phonon softening of graphene under tensile strain is investigated based on ab initio density functional theory calculations. We demonstrate that, over a wide range of tensile strain directions, the strain-induced enhancement of phonon softening can give rise to phonon instabilities resulting in a mechanical failure of graphene. It is shown that there are two types of instabilities associated with phonons near K and Γ points, respectively, which induce symmetry-breaking structural distortions, and both of them lead to mechanical failure prior to the elastic failure commonly expected when the structural symmetry is retained.