Chapter 4 - Atomistic-Continuum Theory

Abstract

In view of the high cost of atomistic simulation when simulating physical behaviors and mechanical properties for large-scale carbon nanotubes (CNTs), this chapter aims to present an atomistic-continuum theory based on the higher-order gradient theory, linking the deformation of the lattice vectors of crystal to that of a continuum deformation field. The involved second-order gradient can exactly capture the bending effect so that this developed atomistic-continuum model is much more reasonable and found to be successful in the study of structural and elastic properties of CNTs. By combining mesh-free methods, a mesh-free computational framework based on the atomistic-continuum theory is developed to simulate local buckling, global buckling, and fracture behaviors of CNTs under typical load, such as hydrostatic pressure, axial compression and tension, torsion, and bending. The atomistic-continuum theory is also capable of studying the free vibration of CNTs and is found to be in a good agreement with full atomic simulation.