Abstract: The effects of the elastic deformation on the mechanical and physical properties of graphene are a subject of intensive current studies. Nevertheless, the stability range for a flat graphene sheet subjected to in-plane deformation is still unknown. Here, this problem is solved by atomistic simulations. In the three-dimensional space corresponding to the E \textgreater (xx) , E \textgreater (yy) , and E \textgreater (xy) components of the planar strain tensor, the surface bounding the stability range for a flat graphene sheet has been constructed disregarding the thermal vibrations and the effects of boundary conditions. For the points of this surface, force components T (x) , T (y) , and T (xy) have been calculated. It is shown that graphene is structurally stable up to strains on the order of 0.3-0.4, but it is unstable with respect to the shear in the absence of stretching forces. In addition, graphene cannot preserve its flat shape under the effect of a compressive force since it has zero flexural stiffness.

Keywords: suspended graphene; strength; ripples

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