Bending and shear moduli of single-walled carbon nanotubes

Abstract

Elastic properties of single-walled carbon nanotubes (SWCNT) obtained experimentally and computationally are reviewed. Attention is paid particularly on the evaluation of Young's and shear moduli of SWCNT. A finite element method (FEM) previously presented by Li and Chou is modified with the Poisson's ratio effect included in the determination of Young's modulus and shear modulus of SWCNT. It is pointed out that within the linear regime, the Young's and shear moduli of SWCNT have been estimated to be constant. This is in contrast to those appeared in the literature in which a wide range of Young's moduli of SWCNT has been reported. The important implications are that the classical theory of elasticity can be employed in the determination of Young's and shear moduli of elasticity of SWCNT, and that nanosensors, nanodevices, and advanced materials embedded with SWCNT can be designed without resort to adopting the uncertain Young's and shear moduli of SWCNT. The modified FEM of treating the SWCNT as a spatial cylindrical frame structure is very simple to use, very economical, and efficient computationally compared with those based on particle or molecular dynamics (MD) methods, simulation and continuum mechanics (CM) methods where huge computational resources are necessary.