Single-walled carbon nanotube modelling based on one-and two-dimensional Cosserat continua
Zhang, Yu (2011) Single-walled carbon nanotube modelling based on one-and two-dimensional Cosserat continua. PhD thesis, University of Nottingham.
This research aims to study the mechanical properties of single-walled carbon nanotubes. In order to overcome the difficulties of spanning multi-scales from atomistic field to macroscopic space, the Cauchy-Born rule is applied to link the deformation of atom lattice vectors at the atomic level with the material deformation in a macro continuum level. Single-walled carbon nanotubes are modelled as Cosserat surfaces, and modified shell theory is adopted where a displacement field-independent rotation tensor is introduced, which describes the rotation of the inner structure of the surface, i.e. micro-rotation. Empirical interatomic potentials are applied so that stress fields and modulus fields can be computed by the derivations of potential forms from displacement fields and rotation fields. A finite element approach is implemented. Results of simulations for single-walled carbon nanotubes under stretching, bending, compression and torsion are presented. In addition, Young’s modulus and Poisson ratio for graphite sheet and critical buckling strains for single-walled carbon nanotubes are predicted in this research.
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