arXiv subjects

Antonino Favata

Publications and source records attributed to Antonino Favata.

22 records · Page 2Linked to original sources

arXiv2011

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.

cond-mat.mes-hall↗

arXiv2011

A New CNT-Oriented Shell Theory

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.

math-ph↗

arXiv2010

On shear and torsion factors in the theory of linearly elastic rods

Lower bounds for the factors entering the standard notions of shear and torsion stiffness for a linearly elastic rod are established in a new and simple way. The proofs are based on the following criterion to identify the stiffness parameters entering rod theory: the rod's stored-energy density per unit length expressed in terms of force and moment resultants should equal the stored-energy density per unit length expressed in terms of stress components of a Saint-Venant cylinder subject to either flexure or torsion, according to the case. It is shown that the shear factor is always greater than one, whatever the cross section, a fact that is customarily stated without proof in textbooks of structure mechanics; and that the torsion factor is also greater than one, except when the cross section is a circle or a circular annulus, a fact that is usually proved making use of Saint-Venant's solution in terms of displacement components.

math-ph↗

arXiv2009

Energy Splitting Theorems for Materials with Memory

We extend to materials with fading memory and materials with internal variables a result previously established by one of us for materials with instantaneous memory: the additive decomposability of the total energy into an internal and a kinetic part, and a representation of the latter and the inertial forces in terms of one and the same mass tensor.

math-ph↗