MICROMORPHIC MODEL OF GRAPHENE-LIKE TWO-DIMENSIONAL ATOMIC CRYSTALS

A novel mechanical model is proposed for graphene-like two-dimensional (2D) atomic crystals based on micromorphic continuum theory, in which the macro-displacement and micro-deformation of a basal element in the Bravais cell of finite size are considered. The governing equations of the model are derived from the basic equations of micromorphic theory in global coordinates. For the Bravais cell of graphene-like crystals containing two atoms, the secular equations of phonon dispersions are then obtained in micromorphic form by analyzing the relations between the vibrational modes of phonons and the independent degrees of freedom of the basal elements, and are further simplified according to the properties of phonon dispersion of 2D crystals, thus the constitutive equations of the model are conformed. Finally, the material constants are determined respectively by fitting the data of the in-plane phonon dispersion relations of graphene and monolayer hexagonal boron nitride with the simplified expressions. The obtained equivalent Young's modulus and Possion' ratio of graphene are 1.05 TPa and 0.197 respectively, and those of monolayer hexagonal boron nitride are 0.766 TPa and 0.225 respectively; both show good agreements with available experimental values.