Hyperelastic behavior of single wall carbon nanotubes

Single wall carbon nanotubes (SWNTs) are shown to obey a hyperelastic constitutive model at moderate strains and temperatures. The finite temperature is considered via the local harmonic approach. The equilibrium configurations were obtained by minimizing the Helmholtz free energy of a representative atom in an atom-based cell model. While the concept of strain-dependent tangent modulus using linear elasticity was considered in prior literature, a constant μ for Ogden's hyperelastic model [R. W. Ogden, Nonlinear Elastic Deformation (Horwood, England, 1984)] is found in the current work for large tubes subjected to moderately large strains up to 900 K.