A Hyperelastic Description of Single Wall Carbon Nanotubes at Moderate Strains and Temperatures

Abstract

In this work, single wall carbon nan- otubes (SWNTs)are shown to obey a hyperelastic constitutive model at moderate strains and tem- peratures. We consider the finite temperature ef- fect via the local harmonic approach. The equi- libriumconfigurationswere obtainedby minimiz- ing the Helmholtz free energy of a representative atom in an atom-based cell model. We show that the strain energy can be fitted by two cubic poly- nomials,which consequentlyproduces for thelin- ear elasticity a linearly increasing tangent modu- lus below a critical strain and an almost linearly decreasing tangent modulus beyond the critical strain. To avoidthestraindependenttangentmod- ulus, we propose to use Ogden's hyperelasticity model to describe the mechanical behaviors of SWNTs. Our results indicate a constant μ for Ogden's hyperelastic model for moderately large strains forlarge tubes and below 900 o K. Thearm- chair tubes are shown to be much stronger and stiffer, but less ductile than the zigzag tubes. We also show that small tubes are more ductile but less stronger. Small tubes and high temperatures reveal more nonlinearity.