An Atomistic-Based Nonlinear Plate Theory for Hexagonal Boron Nitride
Kun Huang, Jiye Wu, Yajun Yin
Abstract
Through the continuity of the DREIDING force field, we propose, for the first time, the finite-deformation plate theory for the single-layer hexagonal boron nitride (h-BN) to clarify the atomic source of the structure against deformations. Divergent from the classical Föppl-von Karman plate theory, our new theory shows that h-BN's two in-plane mechanical parameters are independent of two out-of-plane mechanical parameters. The new theory reveals the relationships between the h-BN's elastic rigidities and the atomic force field: (1) two in-plane elastic rigidities come from the bond stretching and the bond angle bending; (2) the bending rigidity comes from the inversion angle and the dihedral angle torsion; (3) the Gaussian rigidity only comes from the dihedral angle torsion. Mechanical parameters obtained by our theory align with atomic calculations. The new theory proves that two four-body terms in the DREIDING force field are necessary to model the h-BN's mechanical properties. Overall, our theory establishes a foundation to apply the classical plate theory on the h-BN, and the approach in this paper is heuristic in modelling the mechanical properties of the other two-dimensional nanostructures.