Derivation of the Young's and Shear Moduli Ofsingle-Walled Carbon Nanotubes Through a Computational Homogenization Approach

Khoury, Elie El; Messager, Tanguy; Cartraud, Patrice

doi:10.1615/intjmultcompeng.v9.i1.80

Cited by 12 publications

(3 citation statements)

References 47 publications

(93 reference statements)

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“…In Case #1, the longitudinal, transverse, and shear modulus of SWCNT are estimated as 2099.48±0.02, 151.02±0.01, and 720.25±0.06 GPa, respectively, as shown in Table 2. The longitudinal and transverse moduli are close to the simulation results of 2000 and 142 GPa, respectively, and the shear modulus is in the range of 550-860 GPa [72][73][74]. With the decrease of temperature and pressure in other cases, there is no obvious variation of the longitudinal, transverse, and shear stresses.…”

Section: Nano-mechanical Analysissupporting

confidence: 76%

Multiscale Simulation of Temperature- and Pressure-dependent Nonlinear Dynamics of PMMA/CNT Composite Plates

Wang

Shi

Liu

et al. 2021

Preprint

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Owing to the excellent mechanical properties, polymethyl methacrylate (PMMA)/carbon nanotube (CNT) composite has been increasingly adopted in the aerospace field, which is usually subjected to various temperature conditions and supersonic aerodynamic loads. Using a molecular dynamics (MD)-based multiscale simulation, the nonlinear forced vibration of PMMA/CNT composite plate is investigated under coupled temperature and aerodynamic loads conditions. The longitudinal, transverse, and shear moduli of PMMA/single-walled CNT (SWCNT) nanocomposite obtained from MD simulation at different temperature and pressure levels are substituted into the extended rule of mixtures to establish the constitutive equations of PMMA/CNT composite plate. Meanwhile, Poisson’s ratio and thermal expansion coefficient of nanocomposite are used in the constitutive equations. Based on the third-order shear deformation theory, von-Karman nonlinear strain-displacement relation, and Hamilton’s principle, the partial differential equation of composite plate is derived, which is reduced into a set of coupled ordinary differential equations by applying Galerkin method and is solved using the fourth-order Runge-Kutta method. The phase portraits and time histories of composite plate are obtained under the complex loads including transverse harmonic excitation and aerodynamic pressure, which are applied to analyze the dynamic characteristics of system. This study reveals the nonlinear dynamic characteristics of PMMA/CNT composite plate, which contributes to the prediction of long-term performance of composite materials in aerospace field.

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Section: Nano-mechanical Analysissupporting

confidence: 76%

Multiscale Simulation of Temperature- and Pressure-dependent Nonlinear Dynamics of PMMA/CNT Composite Plates

Wang

Shi

Liu

et al. 2021

Preprint

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“…For this purpose, an armchair SWCNT (5,5) with the mechanical properties, including density kg.nm . For CNTs with a diameter longer than nm 3 , the shear modulus becomes constant with the approximate value of 498 Gpa [72]. Table 1 shows the effect of aspect ratio ( / l D ) on the first four nondimensional natural frequencies.…”

Section: Resultsmentioning

confidence: 99%

Effect of External Moving Torque on Dynamic Stability of Carbon Nanotube

Hosseini

Khosravi

Ghadiri

2020

JNanoR

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In nano-dimension, the strength of the material is considerable, and the failure is unavoidable in a torsional mode. Because of this reason, the free and forced torsional vibrations of single-walled carbon nanotube (SWCNT) are investigated in this paper. For dynamic analysis, the moving harmonic torsional load is exerted to SWCNT. The related boundary condition and equation of motion are derived by Hamilton’s principle, and the equation is discretized by the Galerkin method. In order to demonstrate the nonlocality and small–scale effect, Eringen’s theory based on nonlocal elasticity theory is applied. A clamped-clamped (C-C) boundary condition is fitted for the end supports. The influences of the aspect ratio and mode number on the free natural frequency are investigated. Furthermore, the dynamic effects of nonlocal parameter, velocity, thickness, length, and excitation-to-natural frequencies on dimensional and nondimensional angular displacements are indicated. Moreover, the natural frequency was investigated due to the variation of the aspect ratio.

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“…In fact, this type of structures constitutes an optimal trade-off between strength and stiffness, on one side, and lightness, economy and manufacturing times, on the other. By these features they are frequently adopted in civil and industrial buildings, naval, aerospace and bridge constructions, material design and bio-mechanics (Salmon et al (2008), Cao et al (2007), Salehian et al (2006), Cheng et al (2013), Tej and Tejová (2014), Fillep et al (2014), Zhang et al (2016), El Khoury et al (2011, Syerko et al (2013), Ju et al (2008)). In addition, the main component of the railway infrastructure, namely the track, has a periodic character and is often designed against the thermal buckling phenomenon assuming that rails, sleepers and fastenings are part of an infinitely long Vierendeel girder constrained to the ground by springs representative of the ballast actions.…”

Section: Introductionmentioning

confidence: 99%

A direct technique for the homogenization of periodic beam-like structures by transfer matrix eigen-analysis

Gesualdo

Iannuzzo

Penta

2018

Lat. Am. j. solids struct.

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To homogenize lattice beam-like structures, a direct approach based on the matrix eigen-and principal vectors of the state transfer matrix is proposed and discussed. The Timoshenko couple-stress beam is the equivalent continuum medium adopted in the homogenization process. The girders unit cell transmits two kinds of bending moments: the first is generated by the couple of the axial forces acting on the section nodes, the other one is due to the moments directly applied at the node sections by the adjacent cells. This latter moment is modelled as the resultant of couple-stress. The main advantage of the method consists in to operate directly on the sub-partitions of the unit cell stiffness matrix. Closed form solutions for the transmission principal vectors of the Pratt and X-braced girders are also attained and employed to calculate the stiffnesses of the related equivalent beams. Unit cells having more complex geometries are analysed numerically. As a result, the principal vector problem is always reduced to the inversion of a well-conditioned (3 3)  matrix employing the direct approach. Hence, no ill-conditioning problems, affecting all the known transfer methods, are present in the proposed method. Finally, comparing the predictions of the homogenized models with the finite element (f.e.) results of a series of girder, a validation of the homogenization method is performed.

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Derivation of the Young's and Shear Moduli Ofsingle-Walled Carbon Nanotubes Through a Computational Homogenization Approach

Cited by 12 publications

References 47 publications

Multiscale Simulation of Temperature- and Pressure-dependent Nonlinear Dynamics of PMMA/CNT Composite Plates

Multiscale Simulation of Temperature- and Pressure-dependent Nonlinear Dynamics of PMMA/CNT Composite Plates

Effect of External Moving Torque on Dynamic Stability of Carbon Nanotube

A direct technique for the homogenization of periodic beam-like structures by transfer matrix eigen-analysis

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