Abstract
This paper aims at developing a mathematic model to characterize the mechanical properties of single-walled carbon nanotubes (SWCNTs). The carbon-carbon (C–C) bonds between two adjacent atoms are modeled as Euler beams. According to the relationship of Tersoff-Brenner force theory and potential energy acting on C–C bonds, material constants of beam element are determined at the atomic scale. Based on the elastic deformation energy and mechanical equilibrium of a unit in graphite sheet, simply form ED equations of calculating Young's modulus of armchair and zigzag graphite sheets are derived. Following with the geometrical relationship of SWCNTs in cylindrical coordinates and the structure mechanics approach, Young's modulus and Poisson's ratio of armchair and zigzag SWCNTs are also investigated. The results show that the approach to research mechanical properties of SWCNTs is a concise and valid method. We consider that it will be useful technique to progress on this type of investigation.
Highlights
Since the discovery by Iijima in 1991 [1], carbon nanotubes (CNTs) have generated huge activities in most areas of science and engineering due to their unprecedented mechanical, electrical, and thermal properties [2,3,4,5,6,7,8,9,10,11,12,13]
The continuum mechanics seems to be a better way to investigate the properties of CNTs
For armchair SWCNTs, the stretch deformations of the bonds caused by concentrated force and bending moment are schematically signed in Figure 5(a) to analyze Poisson’s ratio
Summary
Since the discovery by Iijima in 1991 [1], carbon nanotubes (CNTs) have generated huge activities in most areas of science and engineering due to their unprecedented mechanical, electrical, and thermal properties [2,3,4,5,6,7,8,9,10,11,12,13]. A different potential model was used by Yao and Lordi [16] who obtained Young’s modulus of CNTs as 1 TPa. MD method has been widely used in simulating the properties of nanostructural materials, it is complex and time consuming, especially for large amount atomic systems. The continuum mechanics seems to be a better way to investigate the properties of CNTs. for the case of nanoreinforced adhesives, these models cannot accurately describe the influence of the relationship between carbon atoms upon the mechanical properties and their interactions in the composite systems because they lack the appropriate constitutive relations that govern material behavior at this scale [30]. The mechanical properties of SWCNTs, including Young’s modulus, Poisson’s ratio, the length of C−C bonds and the angle between the adjacent C−C bonds are discussed as functions of nanosized structure
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