Structural Mechanics Approach Research Articles

Prediction of Fracture Pattern in Defective Single Walled Carbon Nanotubes Using Molecular Structural Mechanics

An atomistic-based dynamic crack model for recreating execution of carbon nanotubes by considering vacancy defects is projected. The idea of the fracture model is taking into account the supposition that carbon nanotubes, when stacked, carry on like space-casing structures. The finite element method is utilized to analyse the nanotube structure and the molecular structural mechanics approach with beam element is used to simulate the non-linear force field of the C–C bonds. The model has been applied to defected single walled chiral, arm chair and zigzag nanotubes subjected to critical tension. The defect presented here (model) is one absent atom at the centre of the nanotube. The anticipated crack advancement, failure stresses of the nanotubes correspond exceptionally well with sub-atomic mechanics model from the literature.

Effect of Stone-wales and Vacancy Defect in Double Walled Carbon Nanotube for Mass Sensing

This paper deals with studying the mass sensing characteristics of defective Double Walled carbon Nanotubes (DWCNTs) using a molecular structure mechanics approach. In this study, vibrational behavior of defective DWCNTs are studied. Two types of defects i.e. Stone-Wales (S-W) and vacancy defects with different location are considered in the present investigation. The interlayer separation in the form of Van der Waals interaction is modelled using characteristic spring element. The inner and outer walls of the nanotube are modelled as elastic beams with a spring element connecting the two layers. Two types of boundary conditions, i.e. cantilever and bridged are considered for the purpose of analysis. In this paper, the effect of S-W defect and Vacancy defect of armchair, zigzag and chiral Double-walled carbon nanotubes (DWCNTs) was studied using an atomic- finite element model based on Molecular Structural Mechanics approach. It is observed that for all three types i.e. Armchair, Zigzag and Chiral nanotubes, the effect of both the type of defect is maximum when it is nearer to the fixed end. The model has been validated with the existing literature.

Numerical stability analysis of imperfect single-walled carbon nanotubes under axial compressive loads

Purpose – A computational structural mechanics approach, based on the exclusive use of standard bar elements is utilized in order to investigate the elastic stability of single-walled carbon nanotubes (SWCNTs) with atom vacancy defects under axial compressive loads. The paper aims to discuss this issue. Design/methodology/approach – The proposed model uses three dimensional, two nodded, linear truss finite elements of three degrees of freedom per node to represent the force field appearing between carbon atoms due to the basic interatomic interactions. Findings – Numerical results concerning the critical forces which cause instability of pristine nanotubes are compared with corresponding data given in the open literature in the effort to demonstrate the good accuracy of the method. Then, it is assumed that SWCNTs present-specific structural defects defined by their length, width, orientation and longitudinal position. The influence of these four geometric parameters of the imperfections considered on the stability of SWCNTs is investigated in detail and essential conclusions are revealed. Originality/value – To the authors’ best knowledge, is the first time that the specific method is introduced for the prediction of buckling behavior of defective SWCNTs. The structural defect here is considered as atoms vacancy that forms a like-crack defect having a specific length, width, orientation and position along the nanotube length.

Analysis of macromolecular microtubules using the potential-based matrix displacement method

This work presents an efficient matrix displacement approach for simulation of microtubules, a typical polyatomic macromolecular bio-structure in eukaryotic cells. The microtubule is modeled as an interatomic potential-based mechanical system. Unlike most of the continuum-based methods, the description of material properties in this model is based on fictitious bond and the interatomic potential energy is considered as based on the atomic force integral between basic macromolecule components. Meanwhile, superior to the conventional atomic-based simulation, the equilibrium state is solved in an efficient matrix framework comparable to the continuum-based structural mechanics approach. Following this approach, free vibration behavior of microtubules is intensively investigated. Microtubules with different boundary restrictions are considered in case studies and vibration modes and frequencies are obtained and compared with available references. It is found that the proposed macromolecular model performs with both accuracy and efficiency, and is superior to the two simulation regimes in atomic scale and continuum level.

Wave propagation in carbon nanotube intramolecular junctions: finite element calculations

The dispersion of longitudinal and transverse waves in (n,0)–(2n,0) intramolecular junctions (IMJs) are investigated using an atomistic finite element method (FEM). The transient responses of IMJs with different connection types subjected to harmonic incident wave were modelled using three-dimensional elastic beams of carbon bonds and point masses. The linkage between the force-field constants of molecular mechanics and input parameters of beam and mass elements was established through the molecular structural mechanics approach. The wave dispersion simulated by FEM shows good agreement with that of the non-local elastic model in a wide frequency range up to the terahertz region. It is shown that both the microstructure of conical part (connection part) and the coupling of longitudinal vibration and transverse vibration brought by the conicity play important roles in the dispersion of longitudinal and transverse wave in a single-walled IMJ. The amplitude decay of longitudinal wave depended on the distance propagating; the wavelength and the structure in connection part are examined. The results show that the dispersion of the decay of the wave amplitude in IMJ with less pentagon–heptagon defects has a better agreement with analytical results of macroscopic conical shell.

Detection of biological objects using dynamic characteristics of double-walled carbon nanotubes.

This study explores double-walled carbon nanotubes as the sensing devices for biological objects including viruses and bacteria. The biological objects studied include alanine with amino terminal residue, deoxyadenosine with free residue, Coronaviridae and Bartonella bacilliformis. An expression has been articulated to identify the mass of biological objects from the shift of frequency. Sensitivity of the sensor has been calculated when subjected to such biological objects. Molecular structural mechanics approach has been used for investigating the vibrational responses of zigzag and armchair double-walled carbon nanotube-based nano biosensors. The elastic properties of beam element are calculated by considering mechanical characteristics of covalent bonds between the carbon atoms in the hexagonal lattice. Spring elements are used to describe the interlayer interactions between the inner and outer tubes caused due to the van der Waals forces. The mass of each beam element is assumed as point mass at nodes coinciding with carbon atoms at inner and outer wall of DWCNT. Based on the sensitivity and the frequency shift it can be concluded that cantilever zigzag DWCNTs are better candidates for detecting the biological objects.

Application of the molecular mechanics method to simulation of buckling of single-walled carbon nanotubes

The molecular mechanics (MM) method based on the Modified Morse force field is used to determine the critical buckling parameters and post-critical deformation modes of single-walled carbon nanotubes (SWCNTs) twisted at the edges. Computer simulation of the buckling and post-critical deformation of nanotubes is performed using two versions of the MM method: the standard MM method and a mixed method combining the molecular mechanics and molecular structural mechanics approaches (MM/MSM method). Computer simulation shows that the MM/MSM method gives acceptable critical twisting angles, buckling modes, and post-critical deformed configurations of nanotubes, comparable to the critical twisting angles, modes, and configurations obtained using the standard MM method. More precisely, for the (10,10) armchair SCWNT 12.2919nm long, the solutions obtained by both methods are similar up to the beginning of fracture of the SCWNT (at a twisting angle up to 240° for each edge), and for the (10,0) zigzag SCWNT 16.8980nm long, the solutions obtained by both methods are similar up to the final twisting angle of 360° for each edge. The critical linear twisting angle for the (10,10) armchair SWCNT obtained in the present study is compared with the critical linear twisting angles obtained by other authors using the REBO, DREIDING, and MM3 force fields. It is concluded that the critical linear twisting angle obtained in the present study using the Modified Morse force field is unrealistically underestimated compared to the critical linear twisting angles obtained by other authors using the REBO, DREIDING, and MM3 force fields.

Mechanical vibrations of carbon nanotube-based mass sensors: an analytical approach

Purpose – The purpose of this paper is to examine the potential of single-walled carbon nanotubes as mass sensors by developing analytical expressions and then comparing the outcome with structural mechanics corresponding predictions. Design/methodology/approach – The carbon nanotube (CNT) resonators are assumed to be either single or double clamped. Analytical formulas capable of describing the vibrational behavior of such CNT-based nanoresonators with an attached mass at nanotube tip or various intermediate positions are developed by combining the Euler–Bernoulli theory and Krylov–Duncan functions. Findings – The validity and the accuracy of these formulas are examined for a wide range of cases via comparisons with corresponding results arisen by spring- or beam-based structural mechanics predictions. Both structural mechanics approaches utilize three-dimensional nanoscale elements formulated according to the molecular theory. The results indicate that the new sensor equations may be utilized for the estimation of vibration response of CNT-based mass sensors with reasonable accuracy. Originality/value – Simple analytical formulas are proved to approximate the mass sensing ability of CNTs adequately, the fact that may significantly contribute in the effort of developing new sensor devices.

Mechanical properties and deformation behavior of carbon nanotubes calculated by a molecular mechanics approach

Carbon nanotubes are due to their outstanding mechanical properties destined for a wide range of possible applications. Since the knowledge of the material behavior is vital regarding the possible applications, experimental and theoretical studies have been conducted to investigate the properties of this promising material. The aim of the present research is the calculation of mechanical properties and of the mechanical behavior of single wall carbon nanotubes (SWCNTs). The numerical simulation was performed on basis of a molecular mechanics approach. Within this approach two different issues were taken into account: (i) the nanotube geometry and (ii) the modeling of the covalent bond. The nanotube geometry is captured by two different approaches, the roll-up and the exact polyhedral model. The covalent bond is modeled by a structural molecular mechanics approach according to Li and Chou. After a short introduction in the applied modeling techniques, the results for the Young\'s modulus for several SWCNTs are presented and are discussed extensively. The obtained numerical results are compared to results available in literature and show an excellent agreement. Furthermore, deviations in the geometry stemming from the different models are given and the resulting differences in the numerical findings are shown. Within the investigation of the deformation mechanisms occurring in SWCNTs, the basic contributions of each individual covalent bond are considered. The presented results of this decomposition provide a deeper understanding of the governing deformation mechanisms in SWCNTs.

Evolution of mesoscopic granular clusters in comminution systems: a structural mechanics model of grain breakage and force chain buckling

A major scientific challenge in establishing a micromechanics theory for complex materials is the characterisation and modelling of emergent mesoscopic phenomena. This study demonstrates the key elements of a structural mechanics approach to the modelling of mesoscopic dissipative phenomena in comminution systems where grain breakage and force chain buckling coexist. Given the many degrees of freedom in these systems, there are multitude of possible configurations and configurational transitions accessible even for a small particle cluster (e.g. a particle and its immediate neighbours). Here, we develop a model of the evolution of a 6-particle cluster undergoing breakage and force chain buckling, in sequence. The analysis lays bare the intricate connections between the contact topology, the relative kinematics arising from the interactions of particles at the bonded versus non-bonded contacts, and the collective dynamics of these interactions as the cluster is monotonically compressed under confinement. The stress-displacement response profiles at the cluster scale exhibit qualitatively similar properties to those seen in macroscopic assemblies under confined compression. A parametric analysis is undertaken to explore the effects of grain-scale resistances to breakage and buckling with respect to the overall force-displacement behaviour of the granular cluster. The study casts light on open problems for future research into the micromechanics of emergent cluster behaviour germane to comminution systems.

The Effect of Atom Vacancy Defect on the Vibrational Behavior of Single-Walled Carbon Nanotubes: A Structural Mechanics Approach

An atomistic structural mechanics method, which is based on the exclusive use of spring elements, is developed in order to study the effect of imperfections due to atom vacancy on the vibrational characteristics of single-walled carbon nanotubes (SWCNTs). The developed elements simulate the relative translations and rotations between atoms as well as the mass of the atoms. In this way, molecular mechanics theory can be applied directly because the atomic bonds are modeled by using exclusively physical variables such as bond stretching. The method is validated for its predictability comparing with vibration results found in the open literature for pristine nanotubes. Then, it is used for the vibration analysis of defective nanotubes. Imperfections such as one-atom vacancy, two-atom vacancy, and one carbon hexagonal cell vacancy are investigated. Their effect on vibrational behavior is explored for different defect positions, nanotube diameters, and support conditions. According to the obtained results, the fundamental frequency is decreased as the size of imperfection increases, and the percentage reduction in fundamental frequency due to the atomic vacancy defect is more affected for a single-clamped SWCNT than for a double-clamped one.

Prediction of Elastic Mechanical Behavior and Stability of Single-Walled Carbon Nanotubes Using Bar Elements

A computationally effective structural mechanics approach based on the exclusive use of bar elements is developed in order to test its efficiency to predict the elastic longitudinal, torsional, and radial mechanical properties of zigzag, chiral, and armchair single-walled carbon nanotubes (SWCNTs). In addition, the proposed method is used for the investigation of the stability of SWCNTs under compressive and radial loads. The proposed model uses three-dimensional, two-noded, linear bar finite elements of three degrees-of-freedom per node to represent the force field appearing between carbon atoms due to the basic interatomic interactions. The numerical results, which are compared with corresponding data given in the open literature, demonstrate the convergence and stability of the method in predicting the elastic properties and critical forces that cause the instability of the tubes. The effect of chirality, length, and radius of carbon nanotubes on numerical predictions is thoroughly and clearly demonstrated.

Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Buckling and Nonlinear Dynamic Examples

For the modeling of large deformations in multibody dynamics problems, the absolute nodal coordinate formulation (ANCF) is advantageous since in general, the ANCF leads to a constant mass matrix. The proposed ANCF beam finite elements in this approach use the transverse slope vectors for the parameterization of the orientation of the cross section and do not employ an axial nodal slope vector. The geometric description, the degrees of freedom, and a continuum-mechanics-based and a structural-mechanics-based formulation for the elastic forces of the beam finite elements, as well as their usage in several static problems, have been presented in a previous work. A comparison to results provided in the literature to analytical solution and to the solution found by commercial finite element software shows accuracy and high order convergence in statics. The main subject of the present paper is to show the usability of the beam finite elements in dynamic and buckling applications.

Effect of uncertainty parameters on graphene sheets Young’s modulus prediction

Software based on molecular structural mechanics approach (MSMA) and using finite element method (FEM) has been developed to predict the Young’s modulus of graphene sheets. Obtained results have been compared to results available in the literature and good agreement has been shown when the same values of uncertainty parameters are used. A sensibility of the models to their uncertainty parameters has been investigated using a stochastic finite element method (SFEM). The different values of the used uncertainty parameters, such as molecular mechanics force field constants kr and kθ, thickness (t) of a graphene sheet and length (LB) of a carboncarbon bonds, have been collected from the literature. Strong sensibilities of 91% to the thickness and of 21% to the stretching force (kr) have been shown. The results justify the great difference between Young’s modulus predicted values of the graphene sheets and their large disagreement with experimental results.

Buckling behavior of perfect and defective DWCNTs under axial, bending and torsional loadings via a structural mechanics approach

The buckling behavior of perfect and defective double-walled carbon nanotubes (DWCNTs) under axial compressive, torsional and bending loadings is investigated using a structural mechanics model. The effects of van der Waals (vdW) forces are further modeled using a nonlinear spring element. Critical buckling loads, critical buckling moments and the effects of vacancy defects were studied for armchair nanotubes with various aspect ratios. The results show that vacancy defects greatly reduce the critical buckling load of DWCNTs. The density of defects plays an important role in buckling of DWCNTs. The results of this numerical model are in good agreement with their comparable existing works.

The Size- and Chirality-Dependent Elastic Properties of Graphene Nanofilms

Tianjin Internal Combustion Engine Research Institute, Tianjin University, Tianjin 300072, ChinaElastic properties of monolayer and multilayer graphene nano“lms are investigated in the paperbased on structural mechanics approach. Via the linkage between the interatomic potential energyin molecular mechanics and the strain energy in classical structural mechanics, the models ofspace frame structures are developed to simulate the graphene crystals. By using “nite elementmethod, Youngs moduli and Poissons ratios of monolayer graphene nano“lms are calculated, andare proved to be size- and chirality-dependent. The values of Youngs moduli and Poissons ratiosshow an agreement with the experimental results in the literatures. In addition, Youngs moduliand Poissons ratios of multilayer graphene nano“lms are simulated to the cases with and withoutsurface relaxation taken into consideration, respectively. The results of calculation show that Youngsmodulus of multilayer graphene nano“lms is size-dependent, and surface relaxation has importantin”uence on it.

The effect of interfacial shear strength on damping behavior of carbon nanotube reinforced composites

The effect of interfacial shear strength (ISS) on the mechanical and damping properties of carbon nanotube reinforced composites (CNT-RCs) is investigated in the present study using a multiscale simulation. The atomic lattice of CNTs is modeled with the modified molecular structural mechanics (MMSM) approach and reduced to an equivalent beam element (EBE) which is used as the basic building block for the construction of full length CNTs embedded in the polymer. Linear material properties are assigned to the EBEs, while a Maxwell–Wiechert material model is used for modeling the viscoelastic behavior of the polymer. The interfacial load transfer mechanism between the lateral surface of the carbon nanotube and the surrounding matrix is taken into account with a nonlinear bond-slip friction-type model. Finite element models of representative volume elements (RVEs) are constructed comprised of two independent meshes: a structured with solid elements for the matrix and a series of embedded EBEs for the full length CNTs inside the matrix. Straight as well as wavy CNTs are considered. In the case of wavy CNTs, random CNT geometries are generated using the spectral representation method with evolutionary power spectra (EPS) which are derived from processing scanning electron microscope (SEM) images. Stochastic average properties were derived with Monte Carlo simulation. The mechanical and damping properties of the CNT-RCs are assessed on the basis of sensitivity analyses with respect to various weight fractions and interfacial shear strength (ISS) values. Numerical results are presented, showing the significant effect of the ISS as well as the influence of CNT waviness on the damping behavior of CNT-RCs.

Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples

In the present paper, a three-dimensional shear deformable beam finite element is presented, which is based on the absolute nodal coordinate formulation (ANCF). The orientation of the beam’s cross section is parameterized by means of slope vectors. Both a structural mechanics based formulation of the elastic forces based on Reissner’s nonlinear rod theory, as well as a continuum mechanics based formulation for a St. Venant Kirchhoff material are presented in this paper. The performance of the proposed finite beam element is investigated by the analysis of several static and linearized dynamic problems. A comparison to results provided in the literature, to analytical solutions, and to the solution found by commercial finite element software shows high accuracy and high order of convergence, and therefore the present element has high potential for geometrically nonlinear problems.

A multiscale approach for estimating the chirality effects in carbon nanotube reinforced composites

In this paper, the multiscale representative volume element approach is proposed for modeling the elastic behavior of carbon nanotubes reinforced composites. The representative volume element incorporates the continuum approach, while carbon nanotube characterizes the atomistic approach. Space frame structure similar to three dimensional beams and point masses are employed to simulate the discrete geometrical constitution of the single walled carbon nanotube. The covalent bonds between carbon atoms found in the hexagonal lattices are assigned elastic properties using beam elements. The point masses applied on each node are coinciding with the carbon atoms work as mass of beam elements. The matrix phase is modeled as a continuum medium using solid elements. These two regions are interconnected by interfacial zone using beam elements. Analysis of nanocomposites having single walled carbon nanotube with different chiralities is performed, using an atomistic finite element model based on a molecular structural mechanics approach. Using the proposed multi scale model, the deformations obtained from the simulations are used to predict the elastic and shear moduli of the nanocomposites. A significant enhancement in the stiffness of the nanocomposites is observed. The effects of interfacial shear strength, stiffness, tensile strength, chirality, length of carbon nanotube, material of matrix, types of representative volume elements and types of loading conditions on the mechanical behavior of the nanocomposites are estimated. The finite element results are compared with the rule of mixtures using formulae. It is found that the results offered by proposed model, are in close proximity with those obtained by the rule of mixtures.

Limit load analysis of graphene with pinhole defects: A nonlinear structural mechanics approach

In this paper, a fully nonlinear spring-based structural mechanics approach, incorporating the modified Morse potential, is presented. Defects are defined as holes developed due to atom vacancies, as opposed to the perfect nanostructure of a graphene sheet. Appropriate boundary conditions are applied to evaluate the proposed method, under tensile and shear loadings, using finite element analysis. Material properties like stress–strain curves and elastic and fracture related properties of both pristine and defective graphene sheets, are predicted. The effect of defect size on mechanical response of the graphene with respect to its zigzag and armchair directions is explored. Analytical expressions of mechanical properties are obtained, using regression analysis of numerical results. The proposed method is validated by comparing predicted properties to data obtained from the literature.