Antonino Favata

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

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.

Elasticity for geotechnicians

Description based on online resource; title from PDF title page (ebrary, viewed October 10, 2013).

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 that 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.

The Kelvin Problem

Lord Kelvin (William Thompson, 1824–1907) solved the problem that was later named after him in 1848. The problem consists in finding the equilibrium state of a linearly elastic, isotropic material body occupying the whole space and being subject to a point load.

On energy and entropy influxes in the Green–Naghdi Type III theory of heat conduction

The energy-influx/entropy-influx relation in the Green–Naghdi Type III theory of heat conduction is examined within a thermodynamical framework à la Müller–Liu, where that relation is not specified a priori irrespectively of the constitutive class under attention. It is shown that the classical assumption, i.e. that the entropy influx and the energy influx are proportional via the absolute temperature, holds true if heat conduction is, in a sense that is made precise, isotropic. In addition, it is proved that influx proportionality cannot be postulated in general, because a counterexample can be given in the case of transversely isotropic conduction.

A shell theory for chiral single-wall carbon nanotubes

In this paper, we propose a characterization of the mechanical response of the linearly elastic shell we associate to a single-wall carbon nanotube of arbitrary chirality. In Favata and PodioeGuidugli (2012), we gave such a characterization in the case of zigzag and armchair nanotubes; in particular, we showed that the orthotropic response we postulated for the associated shells is to become isotropic in the graphenelimit, that is, when the shell radius grows bigger and bigger. Here we give an explicit recipe to construct the generally anisotropic response of the shell associated to a nanotube of any chirality in terms of the response of the shell associated to a related zigzag or armchair nanotube. The expected coupling of mechanical effects that anisotropy entrains is demonstrated in the case of a torsion problem, where the axial extension accompanying twist is determined analytically.

What Shell Theory fits Carbon Nanotubes

We discuss what linearly elastic shell model would bestcapture the peculiarities of the mechanical response of carbonnanotubes, be they single- or multi-wall. We argue that, at themacroscopic scale, carbon nanotubes should be modeled asorthotropic cylindrical shells. An abridged presentation ofthe basic ingredients of such a shell theory is given.

A Shell Theory for Carbon Nanotube of Arbitrary Chirality

This write-up summarizes the developments in Bajaj et al. [1], Favata and Podio-Guidugli [8, 9], along the lines of the presentation recently given by one of us in the occasion of the international conference ‘SMT in MB’. A characterization is given of the mechanical response of the linearly elastic, anisotropic shell we propose to associate to a single-wall carbon nanotube of arbitrary chirality.

A beam theory consistent with three-dimensional thermo-elasticity

We propose a model for thermo-elastic beams, consistent with the theory of linear three-dimensional thermo-elasticity and deduced by a suitable version of the principle of virtual powers. Dimensional reduction is achieved by postulating convenient a priori representations for mechanical and thermal displacements, the latter playing the role of an additional kinetic variable. Such representations are regarded as internal constraints, some involving the first, others, the second, gradient of deformation and thermal displacements; these constraints are maintained by reactive stresses and hyper-stresses of the type occurring in non-simple elastic materials of grade two, and by reactive entropy influxes and hyper-influxes.

One-Dimensional Paradigms

In this introductory chapter, we work in a one-dimensional (1-D) setting. Firstly, we exemplify the nonstandard integration method we are going to use systematically in Part II. Secondly, we exemplify the Green-kernel integration method to be exploited, in particular, for the problems collected in Part III. Finally, we use these two integration methods to solve the 1-D versions of Kelvin’s and Mindlin’s problems.