Structural Mechanics Approach Research Articles

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.

Effect of temperature on vibrations and buckling behavior of carbon nanotube-based mass sensors using a new temperature-dependent structural model

In last decade, structural mechanics (SM) approach has been one of the most known and effective tools for the determination of the mechanical properties of carbon nanotubes (CNTs) such as elastic modulus, shear modulus, natural frequency, and critical axial buckling strain. Considering increasing applications of CNTs as resonators at low and high temperatures, a new temperature-dependent structural mechanics model is presented here. The proposed model can be utilized to predict the effect of temperature on the mechanical response of CNTs as functional resonators. Mechanical and geometrical properties of equivalent beam element are correlated to the CNT's coefficient of thermal expansion (CTE). Owing to elaborate series of finite element simulations, the frequency shift of a CNTs-based mass sensor with different attached mass and aspect ratio in temperature range of 0–1600 K is calculated. Afterwards, the critical buckling temperature of CNTs-based mass sensor due to increasing the axial force by changing ambient temperature is obtained. Results show that decreasing the first natural frequency is clearly appeared by attaching a mass more than about 1 zg on the CNTs structure. In other words, CNTs can be used to detect particles with mass above 1 zg. Moreover, it is shown that the variation of CTE versus temperature is a critical parameter that influences the vibration and buckling behavior of CNTs-based mass sensors. Increasing temperature leads to decreasing natural frequency due to rising axial forces along the CNTs axis. As a result, the natural frequency approaches to zero when the temperature rises up to the critical buckling temperature. In addition, increase in temperature over the critical buckling temperature changes the mode shape of CNT vibration to the next mode shape.

Utilizing a Structural Mechanics Approach to Assess the Primary Effects of Injury Loads Onto the Axon and Its Components.

Diffuse axonal injury (DAI) occurs as a result of the transmission of rapid dynamic loads from the head to the brain and specifically to its neurons. Despite being one of the most common and most deleterious types of traumatic brain injury (TBI), the inherent cell injury mechanism is yet to be understood. Experimental observations have led to the formulation of different hypotheses, such as mechanoporation of the axolemma and microtubules (MTs) breakage. With the goal of singling out the mechanical aspect of DAI and to resolve the ambiguity behind its injury mechanism, a composite finite element (FE) model of a representative volume of an axon was developed. Once calibrated and validated against published experimental data, the axonal model was used to simulate injury scenarios. The resulting strain distributions along its components were then studied in dependence of strain rate and of typical modeling choices such as the applied MT constraints and tau proteins failure. Results show that oversimplifying the MT bundle kinematic entails a systematic attenuation (cf = 2.33) of the computed maximum MT strain. Nevertheless, altogether, results support the hypothesis of axolemma mechanoporation as a cell-injury trigger. Moreover, for the first time the interconnection between the axolemma and the MT bundle is shown to play a role in damage localization. The proposed FE axonal model is a valuable tool to understand the axonal injury mechanism from a mechanical perspective and could be used in turn for the definition of well-informed injury criteria at the tissue and organ level.

Two-Scale Geomechanics of Shale

Summary The geomechanical properties of reservoirs, which are important for formation stimulation, are often determined from triaxial tests on large-scale samples such as core plugs or blocks. It is difficult to recover large samples from shale formations because they are mechanically unstable and usually break down into pieces. The present study develops a two-scale model that uses drill cuttings to estimate the static elastic properties of shales at the core scale. We first propose a physically representative element to capture the elastic deformation of a solid grain with a known minerology by accounting for the grain size and its elastic properties using the structural-mechanics approach (a small-scale model). We then develop a core-scale model dependent on the volume fractions of the minerals, which are obtained from X-ray diffraction (XRD), for different realizations of the spatial distribution of the solid grains (large-scale model). The sensitivity of the large-scale model to the number of the elements is tested. The proposed model shows promising results for four shale formations (New Albany, Rocky Mountain Siliceous, Lower Bakken, and Barnett) and has major applications for the geomechanical characterization of a formation from drill cuttings.

Potential-of-Mean-Force Approach for Molecular Dynamics–Based Resilience Assessment of Structures

AbstractA molecular dynamics (MD)–based structural mechanics approach is proposed for the assessment of resilience of buildings. At the core of the approach, potentials of mean force (PMFs) suitabl...

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.

Quantized prediction of coefficients of thermal expansion of 3-D CNT-Graphene junctioned carbon nanostructures

A computational finite element analysis based on a structural molecular mechanics approach was conducted to predict effective coefficients of thermal expansion (CTE) of a novel three-dimensional carbon nanostructure, pillared graphene structure (PGS), which is constituted with several graphene sheets and single-walled carbon nanotubes. Four sets of representative unitcell models were developed atomistically having different geometric parameters of pillar length and inter-pillar distance in the PGS. Periodic boundary conditions were applied to periodic unitcell geometries to yield consistent results. Parametric study shows that both pillar length and inter-pillar distance significantly affect the effective in-plane and through-thickness CTEs. The PGS with smaller inter-pillar distance and larger pillar length yields higher in-plane CTEs, while that with larger inter-pillar distance and smaller pillar length yields higher through-thickness CTE. The calculation yields negative through-thickness CTE at low temperatures (T<100 K) for all sets of PGSs, which is associated with the curvature at the junction.

Effects of Size and Shape on Elastic Constants of Graphene Sheet

Nanotechnology is used in different engineering fields such as mechanical, aerospace, and civil. One of the most interesting structures which recently have come to the center of attention is the Graphene Sheet (GS). Graphene is a material with high potential of usage in civil structures like structural rehabilitation. In the present paper a finite element based structural analysis program is employed to study the mechanical properties of GS. The advantage of using this method is its simplicity and efficiency in different types of loading. The models considered here are based on a structural mechanics approach by using finite beam elements. Variations of Young's moduli of GS versus different sizes of sheet in two principal directions are investigated. Afterwards, Poisson's ratio and shear modulus for a special case are obtained. The results are consistent with basic structural mechanics theory. Final results reveal the importance of GS size on its Young's modulus, Poisson's ratio and shear modulus. The results are in good agreement with previously published results by other scientists.

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.

Finite element simulation of mechanical properties of graphene sheets

Graphene is the material for the twenty first century applications. In this paper, the elastic properties of monolayer and double layer Graphene sheets, typically less than 10nm in size are investigated through linear finite element simulations. The effect of aspect ratio, sizes and chirality of the Graphene sheet on the Young’s modulus, Shear modulus and Poisson’s ratio are studied. By using structural mechanics approach combining atomistic and equivalent continuum techniques, the Young’s modulus, shear modulus and the Poisson ratio were found and they slightly increase with the aspect ratio but decrease with the size of the Graphene sheet. These simulated properties compliment the mechanical properties of Graphene found in literature.

Geometric–material analogy for multiscale modelling of twisted plates

It is well known that the macroscopic behaviour of many engineering materials is strongly affected by the role of underlying microstructure. Currently though, mathematical expressions linking behaviour of large scale structures to the geometry of their microscopic structure are largely lacking. In this respect, establishing quantitative links across different material lengthscales may offer new pathways for engineering design. In the present work an analogy between cross sectional geometrical properties, representing macrostructure, and a material length parameter, representing microstructure, is presented. The analogy is established through the study of a thin plate subject to axial loading undergoing finite displacements from two alternative perspectives. First, we consider a thin elastic plate with a pretwist about the loading axis where a warping term is introduced accounting for the out-of-plane deformation of the cross section. The coupled governing differential equations and the corresponding coupled boundary conditions are explicitly derived employing a classical structural mechanics approach utilising an energy variational statement. Secondly, an axially loaded thin flat plate (i.e. with no pretwist) is studied with strain gradient elasticity theory incorporating only one material length parameter representing the microstructure, in addition to the two classical Lamé stiffness constants. The ensuing analogy emerges by comparison of the governing equations of the two formulations which shows a mathematical expression can be identified, which incorporates both geometric and material length variables, that formalises the link between microscale and macroscale. This mathematical expression, which constitutes the kernel of the proposed multiscale approach, admits a twofold interpretation depending on the assumed independent variable. On the one hand, the proposed multiscale modelling approach suggests that a plate with complex global geometry can be substituted by a structurally - equivalent, flat plate with constitutive relations given by a non - local, strain gradient theory. On the other hand, the material length parameter can be interpreted on a physical basis because for the first time it has been identified as a known function of geometrical features of the structure through simple algebraic relationships for various cross sectional profiles.

A structural mechanics approach for the phonon dispersion analysis of graphene

A molecular structural mechanics model for the numerical simulation of phonon dispersion relations of graphene is developed by relating the C-C bond molecular potential energy to the strain energy of the equivalent beam-truss space frame. With the stiffness matrix known and further based on the periodic structure characteristics, the Bloch theorem is introduced to develop the dispersion relation of graphene sheet. Being different from the existing structural mechanics model, interactions between the fourth-nearest neighbor atoms are further simulated with beam elements to compensate the reduced stretching stiffness, where as a result not only the dispersion relations in the low frequency field are accurately achieved, but results in the high frequency field are also reasonably obtained. This work is expected to provide new opportunities for the dynamic properties analysis of graphene and future application in the engineering sector.

A Structural Mechanics Approach for the Vibrational Analysis of Single-Layered Graphene Sheets

A structural mechanics approach has been employed to analyze the vibrational behavior of single-layered graphene sheets. By adopting this approach, natural frequencies and mode shapes are obtained for different chirality and imposed boundary conditions. Numerical results from the implemented modeling are examined to provide predictive equations for fundamental frequencies of cantilevered and bridged graphene sheets. With the proposed equations, the natural frequencies can be predicted and are comparable to those obtained from theoretical consideration and experimental results.

Simulation of CNT based mass resonator sensor and investigation on the effect of vacancy defect on sensing performances

In this paper carbon nanotube (CNT) as a mass resonator sensor has been modelled by molecular structural mechanics approach. Then the effect of a single vacancy defect and its position on the sensing performances has been simulated. The simulation shows that the natural frequency shift of the cantileverd CNT, is decreased by the vacancy defect. Besides, when the vacancy gets nearer to the tip of the cantilevered CNT, its effect reduces. Simulations show that the effect of single vacancy defect on bridged CNT, in one-fourth of its length, is equal to the cantilevered one. Choosing smaller CNTs with smaller aspect ratios leads to having sensors with higher sensitivities. Simulations show that there are some positions in cantilevered and bridged CNTs that the effect of vacancy in frequency shift is negligible and the bridged CNTs are less sensitive than cantilevered CNTs to defects.

Mechanical Characterization of Boron-Nitride Nanoribbons via Nonlinear Structural Mechanics

In the present paper, the tensile mechanical behavior of different sized, almost squared shaped, boron nitride nanoribbons is numerically investigated and predicted by using a structural mechanics approach based on the use of appropriate nonlinear potential functions concerning both two-body and three-body interatomic interactions appearing within their nanostructure. According to the proposed method, appropriate spring elements are combined in nanoscale in order to simulate the interatomic interactions appearing within boron-nitride nanostructure. The dimensions of boron-nitride nanoribbons as well as the shape of their edges, which may be armchair or zigzag, have influence on the overall behavior of the nanoribbons. Therefore, the study focuses on the prediction of tensile stress-strain behavior of boron-nitride nanoribbons of different sizes and edge shapes as well as on the estimation of significant corresponding material properties such as Young’s modulus, tensile strength, tensile failure strain and tensile toughness. The numerical results, which are compared with corresponding data given in the open literature where possible, demonstrate thoroughly the important influence of size and chirality of a narrow boron nitride monolayer on its mechanical behavior.