Computation of elastic moduli of graphene monolayer in nonsymmetric formulation using energy-based approach

Abstract

In the paper, elastic moduli of finite-sized graphene monolayers are computed in a nonsymmetric formulation using the lattice statics approach. The motion of atoms due to their interaction is not considered, lattice stability is not studied. The presence of covalent binding is assumed to preserve material structure and all atoms are assigned displacements that correspond to a homogeneous deformation gradient tensor. As a result, the deformation kinematics of graphene is strictly controlled and the material response is defined using a variant of the interatomic interaction potential of the Mie family. The dimensionless parameters of the potential are identified using the coincidence criterion of the experimentally determined Poisson ratio of graphene with an estimated value. The obtained potential parameters are used to determine the elastic properties of a graphene monolayer in a nonsymmetric formulation for low strains and low temperatures. It is shown that the graphene monolayer under homogeneous deformation goes to a nonequilibrium state. In order to provide the potential energy minimum of the specimen in the deformed state, it is necessary to assign displacements to a part of graphene atoms that form one of its “triangular” sublattices relative to atoms of another sublattice, with each sublattice being deformed homogeneously.