Stability Range for a Flat Graphene Sheet Subjected to In Plane Deformation

571 Graphene is a flat monatomic carbon layer where each atom has covalent bonds with its three neighbors (see Fig. 1a). Due to its unique mechanical, physical, and optical characteristics, graphene is promising for different technological applications. In recent years, the effects of significant elastic strains on the mechan ical and physical properties of graphene and other low dimensional carbon based structures were widely studied. These studies are in the mainstream of the actively developing technology based on elastic strains [1]. For example, it has been found that the thermal conductivity of graphene and carbon nanotubes decreases gradually with an increase in the tensile stress [2]. The optical conductivity of graphene is also significantly affected by the applied stress [3]. In [4], the effect of uniaxial stretching deformation on the optical atomic vibration modes of graphene was stud ied by Raman spectroscopy. It was shown that the G and 2D bands exhibit a significant redshift and the G band becomes split into two bands due to the symme try lowering induced by the lattice strain. The ab initio calculations demonstrate that the uniaxial stretch strain of up to 10% does not give rise to the gap in the electron density of states [5], whereas strains can be as high as 03–0.4 [6]. The experimental estimate for the tensile strength of graphene gives a value of 42 N/m [7]. The enhancement of the Young modulus of graphene with the temperature increase from 100 to 500 K was revealed by the molecular dynamics calcu lations [8]. The nonlinear theory of elasticity was for mulated for graphene in [9], where the ab initio calcu lations for the constants involved into the defining relationship are also reported. Linear and nonlinear stiffness coefficients were also calculated for graphene through the use of empirical interatomic potentials [10]. Another version of the nonlinear theory of elas ticity for graphene was suggested in [11] and was com pared to the experimental data within the strain range Stability Range for a Flat Graphene Sheet Subjected to In Plane Deformation