Molecular Structural Mechanics Approach Research Articles

Impact of Atomic Vacancy Defects on Vibrational Characteristics of Chiral MWCNT for Viruses/Bacteria

In this study the authors investigated the vibrations performance of chiral multi-walled carbon nanotubes (MWCNTs). They examined chiral MWCNTs with attached bacteria positioned at both the tip and middle sections of the nanotubes. The main goal of this research was to create a sensor with the ability to detect and distinguish bacteria or viruses that could potentially adhere to the surfaces of chiral MWCNTs. The authors considered two boundary conditions, fixed-fixed and fixed -free for the chiral MWCNT. They utilized a molecular structural mechanics approach. In this approach the vibrational responses of chiral MWCNT-based nano-biosensors with different diameters of the chiral MWCNTs were examined. The study’s objective was to fill research gaps by introducing an innovative approach for detecting defects in chiral MWCNTs through vibrational analysis. They simulated 432 MWCNT samples to investigate the vibrational performance of defective chiral MWCNTs. The results suggested that the first mode of the vibrational frequency of the chiral MWCNT is particularly significant for sensing applications. It was observed that as the percentage of vacancy defects increased, the natural frequency decreased for both boundary conditions.

Numerical Evaluation of the Elastic Moduli of AlN and GaN Nanosheets.

Two-dimensional (2D) nanostructures of aluminum nitride (AlN) and gallium nitride (GaN), called nanosheets, have a graphene-like atomic arrangement and represent novel materials with important upcoming applications in the fields of flexible electronics, optoelectronics, and strain engineering, among others. Knowledge of their mechanical behavior is key to the correct design and enhanced functioning of advanced 2D devices and systems based on aluminum nitride and gallium nitride nanosheets. With this background, the surface Young's and shear moduli of AlN and GaN nanosheets over a wide range of aspect ratios were assessed using the nanoscale continuum model (NCM), also known as the molecular structural mechanics (MSM) approach. The NCM/MSM approach uses elastic beam elements to represent interatomic bonds and allows the elastic moduli of nanosheets to be evaluated in a simple way. The surface Young's and shear moduli calculated in the current study contribute to building a reference for the evaluation of the elastic moduli of AlN and GaN nanosheets using the theoretical method. The results show that an analytical methodology can be used to assess the Young's and shear moduli of aluminum nitride and gallium nitride nanosheets without the need for numerical simulation. An exploratory study was performed to adjust the input parameters of the numerical simulation, which led to good agreement with the results of elastic moduli available in the literature. The limitations of this method are also discussed.

Influence on dynamic behaviour of single layer graphene by Stone wales and pinhole defects

ABSTRACT This paper presents a computational procedure for the determination of the dynamic behaviour of graphene with different types of defects. The lattice of graphene is modelled using the molecular structural mechanics (MSM) approach, where the C–C covalent bonds are replaced by equivalent beam elements. Cantilever and bridged boundary conditions are applied for the analysis. Four types of Stone–Wales (SW) defects such as S-W (555-8), S-W (555-888-3), S-W (555-77-8) and S-W (888-3), and two types of pinhole defects with 6 and 24 elements eliminated are examined on armchair, zigzag and chiral type of graphene sheet. The effect of the structural length of the sheet, chirality and defect type on the vibrational properties of graphene sheets is investigated. The computed results reveal that SW defects produce a high frequency to that of pristine graphene, whereas the effect of pinhole defects is significant as compared to SW defects. The computed results will be useful in nano-resonator-based sensor applications.

Mechanical properties of graphene nanoplatelets containing random structural defects

Graphene nanoplatelets (GNPs) consist of a small number of graphene sheets connected through van der Waals forces and, like graphene, offer exceptional mechanical, thermal and electric properties. In this work, GNPs are considered as potential reinforcements in composites and their equivalent mechanical properties are computed. Similarly to graphene, the mechanical behavior of GNPs is greatly affected by the presence of structural defects and therefore, a parametric investigation is conducted herein. Three types of planar defects are considered: Stone–Wales, single vacancy and double vacancy defects. The examined parameters include the defect type, density, distribution as well as the number of graphene layers. The Molecular Structural Mechanics approach is employed to simulate the lattice of each graphene sheet, where the C–C covalent bonds are modeled by energetically equivalent beam elements. The van der Waals interactions between two carbon atoms belonging to different graphene sheets are modeled using truss elements with mechanical properties based on Lennard-Jones potential. Equivalent properties are computed by employing a homogenization-like procedure and random fields of the stiffness tensor are obtained through the moving window technique. A severe reduction of the stiffness of GNPs is observed for vacancy defects, which also lead to considerable variability. Inplane behavior, which differs greatly from out of plane behavior, is shown to be much more susceptible to the effect of defects.

On the Determination of Elastic Properties of Indium Nitride Nanosheets and Nanotubes by Numerical Simulation

Among the semiconductors formed by a 13th group element and nitrogen, indium nitride (InN) has promising electronic and optical properties, which make it an appropriate material for light-emitting devices and high-speed electronic applications. One-dimensional and two-dimensional InN structures, such as nanotubes and nanosheets, respectively, are expected to present novel advanced characteristics different from those of bulk InN, bringing new prospects in the designs of electronic and optical nanodevices. Despite the difficulties in the synthesis and mass production of the indium nitride nanotubes and nanosheets, the understanding of their properties, including mechanical ones, deserves more research attention, taking into account future perspectives. In this context, the present work is an exploratory study on the numerical evaluation of elastic properties of InN nanosheets and nanotubes, using the nanoscale continuum modelling (also called molecular structural mechanics) approach. The results obtained constitute a solid base for further investigation on the mechanical behaviour of the InN nanostructures, where studies are at an early stage or almost absent.

Elastic Properties of Single-Walled Phosphide Nanotubes: Numerical Simulation Study.

After a large-scale investigation into carbon nanotubes, significant research efforts have been devoted to discovering and synthesizing other nanotubes formed by chemical elements other than carbon. Among them, non-carbon nanotubes based on compounds of the elements of the 13th group of the periodic table and phosphorus. These inorganic nanotubes have proved to be more suitable candidates than carbon nanotubes for the construction of novel electronic and optical-electronic nano-devices. For this reason, until recently, mainly the structural and electrical properties of phosphide nanotubes were investigated, and studies to understand their mechanical behavior are infrequent. In the present work, the elastic properties of single-walled boron phosphide, aluminum phosphide, gallium phosphide and indium phosphide nanotubes were numerically evaluated using a nanoscale continuum modelling (also called molecular structural mechanics) approach. The force field constants required to assess the input parameters for numerical simulations were calculated for boron phosphide, aluminum phosphide, gallium phosphide and indium phosphide nanostructures using two different methods. The influence of input parameters on the elastic properties evaluated by numerical simulation was studied. A robust methodology to calculate the surface elastic moduli of phosphide nanotubes is proposed.

Thermomechanical analysis of the effect of contact forces in heat conduction of composite materials through multiscale contact finite element modeling

The present study proposes a thermomechanical surface contact finite element formulation for studying interfacial heat conductance in correlation to micromechanical contact forces. The proposed methodology is applied for modeling heat surface conductivity of Carbon Nanotubes (CNT). The atomic lattice of CNTs is initially modeled using the molecular structural mechanics approach and reduced to an equivalent 2D continuum element. The equivalent 2D continuum element is used as a robust and efficient surrogate model for the construction of full length CNTs in contact. Coupled structural and heat pde’s have been used to describe the corresponding thermomechanical problem which are discretized using 2D quadrilateral finite elements, along with surface contact elements based on the Node to Node and Node to Segment formulations. The problem has been treated as a nonlinear steady state problem and solved in the frame of a Newton-Raphson incremental-iterative scheme. Extensive sensitivity analysis was performed with respect to several influencing parameters, such as initial contact angle, boundary conditions and CNT overlapping. Based on this analysis, the effect of overlapping and approaching angle on the total heat exchange was quantified. It has been demonstrated that in most cases, increasing the total contact force can produce an almost linear increase in heat exchange. However, in cases of small approaching angles between CNTs an extensive contact force could heavily deform the contacting geometries producing a non-linear heat exchange mechanism.

Determination of fundamental coupled torsional—radial frequency of single-walled carbon nanotubes

Research indicates that single-walled carbon nanotubes have a unique coupled torsional–radial vibration as one of their fundamental modes. Determination of their vibration frequency is required for efficient use of single-walled carbon nanotube in nano-electromechanical systems. However, there is no mathematical expression for these frequencies and their dependence on single-walled carbon nanotube geometry is unknown. This article examines the effect of diameter, length, and chirality on the fundamental coupled torsional–radial vibration frequency of single-walled carbon nanotube using molecular–structural–mechanics–approach, finite element analysis, and regression analyses. Consequently, a first-ever mathematical form of this frequency is derived. The form quickly and accurately predicts these frequencies at 1.5% in-sample, and 7.2% out-sample mean absolute percentage error. single-walled carbon nanotubes’ fundamental coupled torsional–radial vibration frequency is found independent of diameter and inversely proportional to length where the proportionality constant depends on chirality. The coupling of modes and the similarity of the frequency form with cylindrical shell suggest that single-walled carbon nanotube behave like thin shells in these vibrations. A form for effective circumferential shear modulus of single-walled carbon nanotube is also derived. This modulus is found to depend only on the chirality where achiral single-walled carbon nanotubes have higher values than chiral single-walled carbon nanotubes. Proposed mathematical forms can be used for characterization of single-walled carbon nanotubes, determination of single-walled carbon nanotubes’ effective shear modulus, and tuning operational frequency of single-walled carbon nanotube-based nano-electromechanical systems.

Analysis of Carbon Nano Tubes using Molecular Structural Mechanics Approach

Carbon Nano Tubes (CNTs) have a nanostructure with length-to-diameter ratio greater than 1,000,000 exhibiting unusually high toughness and elastic-moduli. Young’s modulus of a single-walled CNT is estimated through Molecular Structural Mechanics Approach is being simulated as a frame-like-structure where primary bonds between successive atoms forms a beam. Properties for FE model are calculated from energy equivalence between molecular and structural mechanics. By validation, computed results match well with the literature. Finite element models such as armchair and zig-zag are established and Young’s-moduli are effectively predicted.

Stress Concentration Factor of Single-Layered Graphene Sheets Containing Elliptical Vacancies

In the present study, potential of finite element based molecular structural mechanics (MSM) for evaluating stress concentration factor of single-layered graphene sheets (SLGSs) with elliptical vacancies is successfully addressed. The MSM approach mimics the interatomic forces of the nanostructure by defining an equivalent frame structure containing beam elements. To obtain the mechanical and cross sectional properties of the equivalent beam, the potential energies of chemical bonds between carbon atoms in the hexagonal lattice of SLGSs are equaled to the strain energies of the beams. This novel proposed approach accurately predicts the stress concentration in graphene sheets with significantly less computational effort in comparison to computational physics methods. Both armchair and zigzag configurations are considered. Furthermore, a comparison between the results obtained by presented MSM approach and theory of elasticity for thin infinite panels having elliptical holes is presented. Influence of chirality, and geometry of elliptical vacancies are investigated in details. Results reveal that MSM approach can successfully predicts stress concentration factor phenomena in nano structures, especially SLGSs. It is seen that chirality has a significant effect on the stress concentration factor so that armchair SLGSs show a larger value of stress concentration.

Advanced molecular structural mechanics model for carbon nanotubes incorporating the 2nd generation REBO potential

Molecular mechanics models like the molecular structural mechanics (MSM) model have been proven to be a valuable tool for the investigation of carbon nanotubes. This class of models is based on a chemical force field representing the bonds present in the structure. Up to now, the underlying chemical force field applied in the MSM model is usually based on harmonic potentials. This simple approach comes with major drawbacks limiting the abilities of the MSM approach. In order to overcome these limitations, the present work integrates the 2nd generation reactive bond order potential (REBO), which is a sophisticated chemical force field, into the MSM approach. The development of this advanced MSM model is given in detail. As a demonstration of its capabilities, the elastic properties of different armchair and zig-zag CNTs are investigated numerically. It was found, that the results for the elastic properties differ significantly with the choice of the underlying chemical force field. The arising differences are discussed and reasons for the occurring behavior are given. The developed advanced MSM approach on the basis of the REBO potential strongly enhances the capabilities of the MSM approach while maintaining its excellent accessibility and applicability together with a low computational effort.

Flexural wave propagation analysis of single-walled carbon nanotubes using molecular structural mechanics approach

In the present study, the flexural wave propagation along single-walled carbon nanotubes (SWCNT) is investigated using molecular structural mechanics approach. The dispersion curves associated to the wave propagation characteristics (i.e., phase velocity versus wave number) of (5,5) and (10,10) armchair test tubes are obtained and compared with the results of the Molecular Dynamics (MD), non-local elastic Timoshenko beam model (NT) and non-local Euler beam model (NE). In addition to the advantages of the present approach such as low computational cost against MD technique and its independency to any extra parameters which have to be experimentally evaluated such as unknown length scales in NT and NE methods, the results show good agreement with the MD results, especially at the high wave number (small wavelength) regimes, which the NT and NE techniques fail to achieve an acceptable predictions.

Simulation of Tensile Behaviors of Bamboo-like Carbon Nanotubes Based on Molecular Structural Mechanics Approach Combining with Finite Element Analysis

A molecular structural mechanics approach combining with finite element analysis (MSM/ FEA) was applied to study the microstructure and tensile behaviors of bamboo-like carbon nanotubes (BCNTs). The mathematical model of tensile behaviors of BCNTs was established based on molecular structural mechanics theory. The deformations of BCNTs, with different diameters and compartments set based on the experimental investigation on BCNT structures synthesized by chemical vapor depositon, under tensile load, were analyzed with ANSYS programmed. Results show that the BCNTs have good tensile properties, and those Young’s modulus can reach 0.84 Tpa. Through the analysis, it can be found that the Young’s modulus of BCNTs depends on the diameters and the length of compartment, which is in good agreement with our experimental tests for the tensile performances of individual BCNT.

How does porosity affect the free vibration of single-layered graphene sheets?

This paper aims to investigate the influence of porosity and length size on the free vibration of single-layered graphene sheets (SLGSs). Frequency analysis is performed using a finite element based molecular structural mechanics (MSM) approach mimicking the SLGSs as frame-like structures constructed out of the beam elements. Defining a porous unit cell, 320 SLGSs with different arrangements and values of porosities and various length sizes ranging from 4 to 32 nm are considered. Results reveal that increasing porosity as well as length size both decrease the natural frequencies of SLGSs, significantly. To improve the applicability of the results, a nonlocal small scale parameter introduced by the analytical solutions for vibration of nanoplates in the literature is calibrated in such a way that the obtained frequencies by MSM match the analytical solutions based on the nonlocal theory of elasticity. Both neural network and genetic programming processes are successfully implemented for the calibration. The proposed calibrated parameter can be easily applied to evaluate the natural frequencies of SLGSs for certain values of porosities and length sizes.

Evaluating the Fracture Pattern in Defective DWCNT Using Molecular Structural Mechanics Approach

Background: This manuscript deals with identifying the fracture pattern in defective Double Walled Carbon Nanotubes (DWCNT). It has been projected in a number of published papers that CNTs always possess defects like vacancies in their structure, hence this type of analysis is helpful in studying the pattern of fracture when subjected to tensile and other types of forces. Method: Molecular structural mechanics approach is used to model the defective DWCNT and finite element method is used to simulate the responses of the non-linear force field of the C–C bonds for analysing the systematic fracture in double walled carbon nanotube structure with beam elements. The model has been studied with reference to arm chair and zigzag DWCNTs with an atomic vacancy and exposed to critical tension. The defect presented here (model) is one lacking atom at the outer tube of the double walled carbon nanotube. Results: The failure pattern is found to be different in all the two types of DWCNTs mainly because of the orientation of the covalent bond between carbon - carbon atoms. This orientation further leads to the change in the stiffness of the bonds which further leads to increase in the stress at the junction and later on failure of the tube. The type of pattern evaluated in this manuscript has not been studied previously in DWCNTs. Conclusion: Catastrophic failure took place after fifteen consecutive iterations, for zigzag and armchair of DWCNT. It shows that Zigzag DWCNT ((14,0)@(8,0)) has better strength compared to Arm chair DWCNT ((8,8)@(6,6)). Keywords: DWCNT, finite element method, systematic fracture, molecular structural analysis, van der Waals, fracture pattern.

Multiscale Modeling-Based Assessment of Elastic Properties of SLGS-Polymer Nanocomposites with Double-Atom Vacancy Defects

In this study, which is a continuation of our earlier work, the effect of double-atom vacancy defects (DAVD) on the elastic properties of single-layered graphene sheets (SLGS)-polymer nanocomposites is assessed by the multiscale modeling. According to the latter approach, the polymer matrix is modeled by finite element approach, while the SLGS and interphase layer are simulated at the atomistic scale by the molecular structural mechanics approach. In view of the Lennard–Jones potential concept, it is assumed that the SLGS and polymer matrix are related by van der Waals reciprocity. The fact that the elastic modulus of a polymer with 5% volume fraction of SLGS is increased by 17 times is demonstrated by numerous simulation results. It is also shown that the elastic modulus of SLGS-polymer nanocomposites with DAVDs is deteriorated with an increase in the number of DAVDs and improved with the increased volume fraction of SLGS.

Determination of random material properties of graphene sheets with different types of defects

Abstract This paper presents a computational procedure for the determination of the stochastic material properties of graphene with different types and density of defects. The lattice of graphene is modeled using the molecular structural mechanics (MSM) approach, which is a continuum based nanoscale modeling technique, where the C-C covalent bonds are replaced by energetically equivalent beam elements. Random fields describing the spatial variation of the anisotropic elasticity tensor of defective graphene sheets are determined using the moving window method and Monte Carlo (MC) simulation. Three types of randomly dispersed defects are examined, namely Stone-Wales (SW), single vacancy (SV) and double vacancy (DV). The effect of window size, defect type and density on the random elastic properties of graphene sheets of area 100 × 100 n m 2 is investigated. The computed results reveal that vacancy defects can reduce the axial stiffness of graphene by approximately 60% with respect to that of pristine graphene, whereas the effect of SW defects is less significant. The computed random elasticity tensors can be assigned to equivalent continuum stochastic finite elements used in the framework of continuum modeling of graphene structures.

Effect of Double-Atom Vacancy Defects on the Elastic Properties of Single-Layered Graphene Sheets

A molecular structural mechanics approach is used to study the effect of double-atom vacancy defects (DAVD) on the elastic properties of zigzag and armchair single-layered graphene sheets (SLGS). To this end, the space frame structure is also adopted to model the interatomic forces of the C–C bonds. The numerical simulation results obtained via the finite element method strongly suggest that double-atom vacancy defects reduce the elastic module of SLGS, which effect weakens with graphene size. Finally, the elastic modulus and Poisson’s ratio of SLGS are found to decrease with the number of DAVDs.

Classifying the impact of progressively evacuating hexagonal lattices of C-C bond in DWCNT-based nano resonators

This paper investigates the effect of gradually vacating a ring of hexagonal lattices containing Carbon–Carbon bond in double-walled carbon nanotube (DWCNT)-based nano resonator. The behaviour of zigzag and armchair DWCNTs have been studied by utilizing the Molecular Structural Mechanics approach for modelling and simulations. The process of vacating is performed on the outer wall of DWCNT by keeping the inner wall length as constant. The resonant frequencies and frequency shift corresponding to the attached masses and different boundary conditions have been analysed. Coaxial mode of vibrations are found to exist at higher values of length ratio, which tends to become non coaxial at lower values of the same. With a higher value of length ratio, a reduction in the frequency shift is observed for lower values of mass and is found to be maximum for approximately 50% reduction in the outer tube. The model suggested has been validated with the published literature.

Atomistic evaluation of the stress concentration factor of graphene sheets having circular holes

Stress concentration factor concept has been developed for single-layered graphene sheets (SLGSs) with circular holes through an atomistic point of view by the application of molecular structural mechanics (MSM) approach. In this approach the response of SLGSs against unidirectional tensile loading is matched to the response of a frame-like macro structure containing beam elements by making an equivalence between strain energies of beam elements in MSM and potential energies of chemical bonds of SLGSs. Both chirality and size effects are considered and the atomistic evaluation of stress concentration factor is performed for different sizes of circular holes. Also, molecular dynamics simulations are implemented to verify the existence and location of the predicted stress concentration. The results reveal that size effects and the diameters of circular holes have a significant influence on the stress concentration factor of SLGSs and armchair SLGSs show a larger value of stress concentration than zigzag ones.