A Simplified Continuum Particle Model Bridging Interatomic Potentials and Elasticity of Solids

Abstract

A continuum particle model correlates the interatomic potential of a crystal lattice with the elastic moduli of the solid, in which discrete atoms are modeled by perfectly bonded continuum particles, named singum, to simulate singular forces by stress in continuum. A singum particle occupies the space of the Wigner Seitz cell of the atom lattice. As the first step, a cutoff of the interatomic potential at the bond length was used to simplify the model, which was demonstrated by a two-dimensional (2D) graphene monolayer. The mass, momentum, and energy equivalence between the discrete system and continuum was investigated, and the effective elasticity of the singum was derived from the interatomic potential. The model was extended to face-centered cubic lattices and generalized to polycrystals by orientational average for three-dimensional (3D) isotropic elasticity. The deterministic relationship between the interatomic potential and singum elasticity creates a method to construct a new interatomic potential directly from the elastic moduli. Using orientational average, the isotropic elasticity of the singum for general atom lattices was obtained. When the singum potential was calibrated by polycrystal diamond, it provided a reasonable estimate of the elasticity of the 2D graphene. This simplified singum model provides a clear physical and mechanical correlation from the interatomic potential to elasticity and can be extended to long-range interatomic interactions.