Atomistic–continuum coupled model for nonlinear tensile behavior of carbon nanotube based on a hyperelasticity theory

In this paper, an efficient approach applied for coupled molecular mechanic (MM) – finite element (FE) multi-scale modeling of single walled carbon nanotube (SWCNT). a single layer graphene has been chosen as the representative volume element (RVE) of SWCNT, AIREBO Empirical interatomic potential is utilized in order to describe interatomic interactions, the strain energy density function at continuum scale is obtained as total interatomic potential per unit of an atomic cell by applying continuum biaxial deformations. the surfaces and curves of strain energy density are attained via fitting a fourth-order polynomial function to quantities of strain energy density. The atomic elastic parameters are obtained through computing second-order derivative of surfaces and curves of strain energy density with respect to strain. To bridge between atomistic (nano-scale) level and continuum (macro-scale) level, the mechanical characteristics are captured in the atomistic level and transferred to the continuum level based on hyperelasticity theory. Stress counters are illustrated for axial tensile deformation up to 10%. Comparing the numerical results of the present multiscale method with MM simulation results are elaborated that the suggested technique produces promising results for SWCNT under tension in finite deformation.

Keywords:

Atomistic–continuum coupled model , Multiscale modelling , Carbon nanotubes , Molecular Mechanics (MM) , Finite Element Method (FEM)