Ideal Strength of graphene under general states of tensile strain*

Phonon softening of graphene under general directional tensile strain is investigated based on ab initio density functional theory calculations. Under a wide range of tensile strain configurations, we demonstrate that phonon instabilities are responsible for the mechanical failure of graphene through the strain-induced enhancement of phonon softening. It is shown that there are two types of phonon instabilities 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.