On a nanoscopically-informed shell theory of single-wall carbon nanotubes

Abstract

This paper proposes a bottom-up sequence of modeling steps leading to a nanoscopically informed continuum, and as such macroscopic, theory of single-walled carbon nanotubes (SWCNTs). We provide a description of the geometry of the two most representative types of SWCNTs, armchair (A-) and zigzag (Z-), of their modules and of their elementary bond units. We believe ours to be the simplest shell theory that accounts accurately for the linearly elastic response of both A-and Z-CNTs. In fact, our theory can be shown to fit SWCNTs of whatever chirality; its main novel feature is perhaps the proposition of chirality-dependent concepts of effective thickness and effective radius.

One-dimensional nonlocal elasticity for tensile single-walled carbon nanotubes: A molecular structural mechanics characterization

“…Chirality-induced anisotropy in chiral SWCNTs has been discussed in many works [43][44][45]. However, only few studies aimed at modeling chiral nanotubes as anisotropic shells [10,46,47] instead of using the more common isotropic models [7,[48][49][50][51][52][53]. Unfortunately, none of these works has included a comparison of the strain field obtained with atomistic simulations and shell models.…”

Asymptotic estimates of buckling radial pressure for multi‐walled carbon nanotubes at different variants of boundary conditions

“…In our study, considering a MWCNT with the large innermost radius nm, we assume that the chirality of each nanotube composing the MWCNT does not affect practically their elastic properties . In that case each wall of the MWCNT may be represented by a thin isotropic shell with the effective thickness h considered as an input independent parameter.…”

“…Recently, Favata and Podio‐Guidugli and Bajaj et al. proposed a new theory of linearly elastic anisotropic shells with potential application to the continuous modeling of CNTs with an arbitrary chirality. In particular, a mechanical model of orthotropic shells depending on two geometrical parameters (thickness and radius) and five constitutive ones, four of which are independent, has been proposed in .…”

“…Later, based on this model, Bajaj et al. have presented a procedure to determine the effective constitutive moduli and the geometric parameters for zig‐zag and armchair SWCNTs represented by orthotropic shells. In particular, it has been shown that increasing a chirality number and, accordingly, a radius of a zig‐zag SWCNT results in convergence of Young's moduli in the axial and circumferential directions to the so‐called ”graphene limit”.…”

A multiphysics and multiscale approach for modeling microcracked thermo-elastic materials

“…A model within the framework of generalized continuum mechanics, as the one we propose, may be computationally efficient, provided that a proper physical meaning of the additional fields is proposed and a constitutive identification for the internal and the external actions is performed [74,64,69,4,27,51,5,2,77]. In the present model, on the purely mechanical side, in addition to the standard displacement field, we consider a kinematical microstructural field, representing the mean jump of the displacement field due to the presence of microcracks; on the thermal side, we not only consider the thermal displacement, a nonstandard thermal state variable firstly considered by Helmholtz, but we also introduce an additional microstructural kinetic variable, whose time derivative represents the mean jump of the temperature field due to the presence of microcracks, and that we can call microtemperature.…”