Hyperelastic finite element model for single wall carbon nanotubes in tension

This paper investigates the hyperelastic behaviour of single wall carbon nanotubes (SWCNTs) by means of a finite element-based lattice approach. A one-term incompressible Ogden-type hyperelastic model is chosen to describe the mechanical response of SWCNTs under tensile loading. In order to determine the material constants of the model, numerical tests are conducted on a representative arrangement of carbon atoms, establishing equality between the Ogden strain–energy and the variation of the Tersoff–Brenner interatomic potential. The material constants determined here are then used in numerical simulations carried out on SWCNTs models. A good predictive capability of the present model is found when the obtained results are compared to published data. A first conclusion obtained from the present work suggests that a value of 0.147 nm for the CC bond equivalent diameter is suitable for the hyperelastic description of SWCNTs. A second conclusion reveals a prediction of 0.51 for the breaking strain of SWCNTs under tension, which is in excellent agreement with results obtained from molecular dynamics simulations and continuum theory.

Research highlights
► This paper investigates the hyperelastic constitutive description of SWCNTs.
► We propose an Ogden strain-energy model for the CC bonds of SWCNTs in tension.
► A good predictive capability of the model is found when compared to published data.
► A 0.147 nm diameter is found suitable for the CC bonds hyperelastic modelling.
► A breaking strain of 0.51 is predicted for the SWCNTs under tension.