Homogenization of a graphene sheet

A continuum model for a graphene sheet undergoing infinitesimal in-plane deformations is derived by applying the arguments of homogenization theory. The model turns out to coincide with that found by various authors with different methods, but it avoids anticipations on the validity of any properly adjusted or generalized Cauchy–Born rule. The constitutive equation for stress and the effective Young’s modulus and Poisson ratio are explicitly given in terms of the bond constants.