Stability analysis of atomic structures

The stability and failure mechanism of a structure at the nanometer scale are important for understanding the mechanical behavior of nanoscale materials and structures. This thesis focuses on the material stability of atomic structures. First, the material stability of pristine carbon nanotubes is investigated at the continuum level by using the crystal elasticity theory. A homogenized continuum model is adopted. The strong ellipticity condition is employed to capture the localized failure of carbon nanotubes. The critical strain and strength predicted are reasonably comparable with experimental estimations.

An atomic material stability theory is developed as the atomistic counterpart of the continuum material stability theory in nonlinear elasticity. A local instability indicator named ``atomic acoustic tensor'' is derived and utilized to detect material failure at the atomic scale. The stability criterion is based directly on the local energetic responses of an atomic site, and resorts to neither the continuum theory nor the pristine lattice. Thus, it is applicable to inhomogeneous atomic systems provided that the site energy can be reasonably defined.

The atomic stability theory is combined with atomistic simulation to gain understanding on crack propagation and fracture as instabilities of bond structures. The atomic acoustic tensor is used as the indicator to detect the local instability at the crack tip, and then to decide bond breaking. Quasi-static crack growth till fracture is simulated by the atomistic finite element method, which is proposed according to the form of bond potential and lattice topology.

An Eshelby-type approximate method is presented for calculating the formation energy of Stone-Wales defects. A formula is derived to show that the energy variation consists of the change of local atomic potential due to bond reconfiguration in the defective region and a higher order correction that represents the influence of the remaining system. The method is utilized to investigate the formation energy distribution in non-uniformly deformed nanotubes and to study the energetic interaction between multiple defects.