Strain-induced instabilities of graphene under biaxial stress

The mechanical properties of graphene are investigated using classical molecular dynamics simulations as a function of temperature T and external stress τ. The elastic response is characterized by calculating elastic constants via three complementary methods: (i) numerical derivatives of stress-strain curves, (ii) analysis of cell fluctuation correlations, and (iii) phonon dispersion analysis. Simulations were performed with two interatomic models: an empirical potential and a tight-binding electronic Hamiltonian. Both models predict that the Poisson's ratio ν of graphene increases monotonically with applied stress. The range of stresses studied spans the entire domain of mechanical stability of the planar structure. Two mechanical instabilities are identified. Under tensile stress, fracture occurs, signaled by the softening of a phonon mode at the Brillouin zone boundary (K point). At the studied temperatures (T < 1500 K), auxetic behavior (ν < 0) appears only at high tensile stresses, near the fracture threshold. Under compressive stress, a spinodal instability associated with long-wavelength wrinkling is observed. Finite-size analysis of this instability at 300 K reveals the existence of a finite surface tension σ in the unstressed membrane, which arises from the anharmonic coupling between out-of-plane and in-plane fluctuations. The surface tension stabilizes the membrane's flat morphology. In the thermodynamic limit, the onset of the wrinkling instability occurs when the compressive stress matches the surface tension (τ = σ). Under this spinodal condition, the area compressibility modulus B is characterized by a scaling law N-1/2, where N is the number of atoms in the simulation cell.