Ultimate strength, ripples, sound velocities, and density of phonon states of strained graphene

We study the dispersion characteristics of strained graphene using many-body interatomic potentials and find: (i) borders of the structural stability of a flat graphene in the three-dimensional space of the strain components ( _xx, _yy, _xy); (ii) sound velocities of strained graphene; and (iii) phonon density of states (DOS) of strained graphene. The border of structural stability of flat graphene is also presented in the space of components of normal and shear membrane forces (T _x, T _y, T _xy). We find that flat graphene is structurally stable under elastic strain up to 0.3-0.4, but it becomes unstable to a shear strain in the absence of tensile components of strain. Also graphene cannot remain flat under compressive membrane forces because its bending stiffness vanishes. We employ the molecular dynamics simulations to study the post-critical behavior of graphene. We demonstrate that ripples with controllable amplitude and orientation can be generated under simultaneous action of shear and tensile membrane forces. Gaps in the phonon DOS are observed when graphene is strained close to the appearance of ripples. Sound velocities of unstrained graphene do not depend on the propagation direction but application of strain makes graphene anisotropic. One of the sound velocities vanishes at the border of the structural stability of graphene meaning that vanishing of sound velocity (or corresponding elastic constant) predicts impending instability.