Difference between bending and stretching moduli of single-walled carbon nanotubes that are modeled as an elastic tube

Abstract

Very-high-strength (60-GPa) carbon nanotube fiber design based on molecular dynamics simulations

A study on the bending stiffness of single-walled carbon nanotubes and related issues

“…8 for reference) the value of the thickness determined in this way may exceed 90% of the radius of the tube, which is obviously in contradiction to the basic assumption of the thin-walled tube model. The same conclusion was also obtained for a (5,5) SWCNT by DiBiasio et al (2007).…”

“…However, as pointed by DiBiasio et al (2007), surface Young's modulus E s bending associated with the lateral bending deformation is 291 N/m, which is 19.3% larger than the surface Young's modulus E s tension associated with the axial stretching deformation (E s tension ¼ 242 N=m). In DiBiasio et al's work, the thickness of the SWCNT has been taken as t =0.075 nm.…”

“…Molecular-mechanics model is a versatile tool to study the mechanical properties of nanosystems (Yakobson et al, 1996;Chang and Gao, 2003;Shen and Li, 2004;DiBiasio et al, 2007). According to the molecular-mechanics model, when the weak bonding energies (i.e.…”

“…However, some recent studies show that such kind of relationship is problematic. DiBiasio et al (2007) carried out the molecular-mechanics simulations for a (5,5) SWCNT under axial stretching (AS) and lateral bending (LB) deformation. It was reported that the relative discrepancy between the values of Young's modulus of SWCNTs determined from the axial stretching and the lateral bending can be as large as 19% when the elastic tube model is used.…”

Transverse vibration of single-layer graphene sheets

“…In contrast to SM approaches, the MM method also allows the natural frequencies of the system in equilibrium to be computed without any requirement to use an equivalent thickness value for the nanostructure. In general, the introduction of the thickness concept in nanomaterials is highly contentious, leading to the well-known 'Yakobson's paradox' [41,42], responsible for the high scattering of Young's moduli and Poisson's ratio results in the open literature.…”