A Hyperelastic Description of Single Wall Carbon Nanotubes at Moderate Strains and Temperatures
Xianwu Ling; and S.N. Atluri

doi:10.3970/cmes.2007.021.081
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 21, No. 1, pp. 81-92, 2007
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Abstract In this work, single wall carbon nanotubes (SWNTs) are shown to obey a hyperelastic constitutive model at moderate strains and temperatures. We consider the finite temperature effect 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. We show that the strain energy can be fitted by two cubic polynomials, which consequently produces for the linear elasticity a linearly increasing tangent modulus below a critical strain and an almost linearly decreasing tangent modulus beyond the critical strain. To avoid the strain dependent tangent modulus, we propose to use Ogden's hyperelasticity model to describe the mechanical behaviors of SWNTs. Our results indicate a constant$\mu$ for Ogden's hyperelastic model for moderately large strains for large tubes and below$900^{\mathrm {o}}$K. The armchair 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.
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