A new CNT-oriented shell theory

Abstract

A theory of linearly elastic orthotropic shells is presented, with potential application to the continuous modeling of Carbon NanoTubes. Two relevant features are: the selected type of orthotropic response, which should be suitable to capture differences in chirality; the possibility of accounting for thickness changes due to changes in inter-wall separation to be expected in multi-wall CNTs. A simpler version of the theory is also proposed, in which orthotropy is preserved but thickness changes are excluded, intended for possible application to single-wall CNTs. Another feature of both versions of the present theory is boundary-value problems of torsion, axial traction, uniform inner pressure, and rim flexure, can be solved explicitly in closed form. Various directions of ongoing further research are indicated.

Electromechanical behavior, end enhancements and radial elasticity of single-walled CNTs: A physically-consistent model based on nonlocal charges

“…Modeling CNTs by means of thin shell elements can lead to effective results (Pantano et al, 2004;Favata and Podio-Guidugli, 2012). Pantano et al (2004) studied single-walled CNTs by means of a isotropic plates finite elements.…”

“…The agreement with available experimental and numerical simulations is proved for varying diameters, CNT length and nonlocal length. Based on the common practice of using continuum models with isotropic material for armchair single-walled (Pantano et al, 2004;Favata and Podio-Guidugli, 2012) and multi-walled CNTs , the CNT is here regarded as a thin cylindrical shell subjected to the electrostatic pressure (Section 6).…”

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

“…Another approach in a specification of the effective thickness has been proposed by Favata and Podio‐Guidugli . They conjecture thickness changes due to changes in inter‐wall separation in MWCNTs.…”

“… 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.…”

“…So, Ru [31] has proposed an anisotropic shell model explaining the chirality dependent mechanical phenomena, and Chang [8] has derived the closed-form expressions for the anisotropic elastic properties of SWCNTs applying a molecular mechanics model. Recently, Favata and Podio-Guidugli [14,15] and Bajaj et al [1] 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 [14].…”