N.K. Anifantis

Radial Stiffness and Natural Frequencies of Fullerenes via a Structural Mechanics Spring-based Method

An atomistic structural mechanics method, which is based on the exclusive use of spring elements, is developed in order to study the radial elastic stiffness and vibrational characteristics of C20, C60, C80, C180, C260, C320, C500 and C720 molecules. According to the obtained results, the radial Youngs modulus decreases non-linearly with respect to the radius of fullerene or equivalently with the number of carbon atoms. Similarly, the natural frequencies of the fullerenes are strongly dependent on their radius and their support conditions. The numerical results are compared with corresponding data given in the open literature, where possible.

On the coupling of axial and shear deformations of single-walled carbon nanotubes and graphene: a numerical study

This paper presents a numerical investigation for the evaluation of elastic coupling of extension and twist in single-walled carbon nanotubes. The carbon nanotubes are modelled according to their atomistic structure. The harmonic approximation is utilized for describing the interaction potential energies. The force field is simulated via suitable straight and torsional springs that express the interatomic interactions and interconnect nodes placed on the atomic positions. By using appropriate boundary conditions, the nanotubes are loaded axially and the resulted twist is numerically predicted using finite element procedures. The numerical outcomes reveal that the stretching deformation of single-walled carbon nanotubes leads to their torsion only for the chiral case. A complete parametric study with respect to geometric characteristics of nanotubes shows that the coupling is strongly dependent on the diameter, chiral angle, and nanotube length. To explain these observations, the inherent graphene sheet geometries used for the generation of single-walled carbon nanotubes are also studied under extension. The results prove similar coupling phenomena occur between extension and in-plane shear. Comparisons with results provided in the open literature are also performed, where possible.

Vibration Analysis of Cracked Beams Using the Finite Element Method

Most of the members of engineering structures operate under loading conditions, which may cause damages or cracks in overstressed zones. The presence of cracks in a structural member, such as a beam, causes local variations in stiffness, the magnitude of which mainly depends on the location and depth of the cracks. These variations, in turn, have a significant effect on the vibrational behavior of the entire structure. To ensure the safe operation of structures, it is extremely important to know whether their members are free of cracks, and should any be present, to assess their extent. The procedures often used for detection are di‐ rect procedures such as ultrasound, X-rays, etc. However, these methods have proven to be inoperative and unsuitable in certain cases, since they require expensive and minutely de‐ tailed inspections [1]. To avoid these disadvantages, in recent decades, researchers have fo‐ cused on more efficient procedures in crack detection using vibration-based methods [2]. Modelling of a crack is an important aspect of these methods.

Finite Element Modeling of Nanotubes

Abstract This chapter presents an integrated computational method for the prediction of the nanoscale mechanical response of nanotubes. According to the proposed numerical approach, the nanotubes are modeled according to their equilibrium atomistic structure while standard structural mechanics principles are adopted. Utilizing molecular theory, the interatomic interactions within the nanotube are simulated via suitable spring elements that connect the nodes placed at the atomic positions. The calculation of elastic properties as well as natural frequencies requires linear approximation, whereas nonlinear formulation is utilized for the investigation of static or dynamic elastoplastic deformations. For the prediction of vibrational problems, the stiffness and mass matrices are constructed according to the nodal positions to make the dynamic equilibrium equation solvable. The natural frequencies and the corresponding modes of vibration are derived by solving the eigenvalue problem for different support conditions. The modeling is regenerative and can provide simulations for different geometric characteristics of the nanotubes. The effectiveness of the proposed computational method is demonstrated by comparisons with relevant results from the literature.

Mechanical characterization of hexagonal boron nitride nanocomposites: A multiscale finite element prediction

In this study, a calculation of the elastic mechanical properties of composite materials reinforced by boron nitride nanosheets is taking place, following the finite elements approach. Composites are specifically composed of two phases of materials, the matrix material and the reinforcing phase, here, consisting of boron nitride monolayers. The simulation of these two materials as well as the interface between them were made in accordance with the micromechanics theory, examining a representative volume element. Specifically, the matrix material is considered as continuous medium and the reinforcing phase, based on its atomistic microstructure, is considered as a discrete medium and was simulated through spring-based finite elements. Something similar occurred with the simulation of the interface region, which is responsible for the load transfer between the two materials. The results of the method were compared with data from other studies and showed good agreement.

An Atomistic-based Spring-mass Finite Element Approach for Vibration Analysis of Carbon Nanotube Mass Detectors

Since their discovery in 1991 by Ijima [1], carbon nanotubes (CNT) have received much attention as a new class of nanomaterials revealing a significant potential for use in a diverse range of novel and evolving applications. Much of the interest in CNTs has focused on their particular molecular structures and their unique electronic and mechanical properties. For example, their elastic stiffness is comparable to that of diamond (1000 GPa), while their strength is ten times larger (yield strength 100 GPa). Furthermore, CNTs conduct heat and electricity along their length with very little resistance, and therefore they act as tiny electrical wires or paths for the rapid diffusion of heat. As a result, progressive research activities regarding CNTs have been ongoing in recent years. For more detail on theoretical predictions and experimental measurements of both mechanical and physical properties, see the comprehensive reviews in [2,3]. The combination of an extremely high stiffness and light weight in CNTs results in vibration frequencies on the order of GHz and THz. There is a wide range of applications in which the vibrational characteristics of CNTs are significant. In applications such as oscillators, charge detectors, field emission devices, vibration sensors, and electromechanical resonators, oscillation frequencies are key properties. An representative application is the development of sensors for gaseous molecules, which play significant roles in environmental monitoring, chemical process control, and biomedical applications. Mechanical resonators are widely used as inertial balances to detect small quantities of adsorbed mass through shifts in oscillation frequency. Recently, advances in lithography and materials synthesis have enabled the fabrication of nanoscale mechanical resonators that utilize CNTs [4,5]. The use of a CNT to make the lightest inertial balance ever is essentially a target to make a nanoscale mass spectrometer of ultrahigh resolution. Building such a mass spectrometer that is able to make measurements with atomic mass sensitivity is one of the main goals in the burgeoning field of nanomechanics. An inertial balance relies only on the mass and does not, therefore, require the ionization or acceleration stages that might damage the molecules being