Elastic modulus tensor, force constant matrix and nanodimensional structures
This paper discusses the relationship between integral elastic characteristics of nanodimensional structures and force constants of interatomic bonds. It is shown that the finite element method can be effectively applied to model the mechanical behavior of bound atomic systems. A discrete model is used to calculate elastic moduli under tension and bending of a linear chain of bound atoms; Young's modulus, Poisson's ratio and shear modulus for graphene are calculated using a central force field and valence force field. The contribution of non-valence bonds to elastic moduli is calculated for graphene. Elastic moduli are calculated for a carbon nanotube under different loading conditions.