Effective bending modulus of carbon nanotubes with rippling deformation

Wang, X.; Zhang, Y.C.; Xia, Xing; Huang, Caihuan

doi:10.1016/j.ijsolstr.2004.04.038

Cited by 54 publications

(33 citation statements)

References 12 publications

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“…The quantum mechanics approaches comprise of the classical molecular dynamics and ab initio techniques. However, the use of classical molecular dynamics requires huge computational resources, and is limited to simulating 10 6 -10 8 atoms for a few nanoseconds (Qian et al, 2002;Wang et al, 2004). Similar limitations characterize the ab initio approach.…”

Section: Introductionmentioning

confidence: 99%

“…Some researchers have attempted to characterize carbon nanotubes based on the effective bending moduli. Wang et al (2004) studied the relation between bending moment and bending curvature of CNTs to describe the variation of effective bending modulus-toYoung's modulus ratio with ripples in nanotubes. Another investigation by Wang et al, 2005a) studied the non-linear bending moment-curvature relationship of CNTs with rippling deformation.…”

Section: Introductionmentioning

confidence: 99%

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Analytical and numerical techniques to predict carbon nanotubes properties

Kalamkarov

Georgiades

Rokkam

et al. 2006

International Journal of Solids and Structures

274

133

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In this paper, two different approaches for modeling the behaviour of carbon nanotubes are presented. The first method models carbon nanotubes as an inhomogeneous cylindrical network shell using the asymptotic homogenization method. Explicit formulae are derived representing Young's and shear moduli of single-walled nanotubes in terms of pertinent material and geometric parameters. As an example, assuming certain values for these parameters, the Young's modulus was found to be 1.71 TPa, while the shear modulus was 0.32 TPa. The second method is based on finite element models. The inter-atomic interactions due to covalent and non-covalent bonds are replaced by beam and spring elements, respectively, in the structural model. Correlations between classical molecular mechanics and structural mechanics are used to effectively model the physics governing the nanotubes. Finite element models are developed for single-, double-and multi-walled carbon nanotubes. The deformations from the finite element simulations are subsequently used to predict the elastic and shear moduli of the nanotubes. The variation of mechanical properties with tube diameter is investigated for both zig-zag and armchair configurations. Furthermore, the dependence of mechanical properties on the number of nanotubules in multi-walled structures is also examined. Based on the finite element model, the value for the elastic modulus varied from 0.9 to 1.05 TPa for single and 1.32 to 1.58 TPa for double/multi-walled nanotubes. The shear modulus was found to vary from 0.14 to 0.47 TPa for single-walled nanotubes and 0.37 to 0.62 for double/multi-walled nanotubes.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical and numerical techniques to predict carbon nanotubes properties

Kalamkarov

Georgiades

Rokkam

et al. 2006

International Journal of Solids and Structures

274

133

View full text Add to dashboard Cite

show abstract

“…For example, the elastic modulus of CNTs is reported to be more than 1 TPa. In addition, they are also particularly flexible in bending and can undergo large elastic deformation without breaking [10]. The investigation of the behavior of CNTs are mainly divided into two groups of computational and experimental approaches.…”

Section: Introductionmentioning

confidence: 99%

On the Buckling Behavior of Curved Carbon Nanotubes

Yengejeh

Kazemi

Öchsner

2015

Mechanical and Materials Engineering of Modern Structure and Component Design

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In this study, numerous armchair and zigzag single-walled carbon nanotubes (SWCNTs) were simulated by a commercial finite element package and their buckling behavior was investigated through performing several computational tests with cantilevered boundary conditions and different bending angles. Both computational and analytical results were compared in the case of straight tubes. It was pointed out that the computational results are in good agreement with the analytical calculations. It was also concluded that the first critical buckling load of both straight armchair and zigzag CNTs increases by increasing the chiral number. In addition, it was indicated that the first critical buckling load of straight CNTs decreases by introducing the bending angle to the structure of CNTs. However, this decrease is more noticeable in the case of armchair and zigzag CNTs with higher number of chirality and it is almost negligible for CNTs with lower number of chirality.

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“…It is well known that the molecular dynamics method (MD) [20,21] has been developed to simulate the properties of the material with microstructures; however, MD simulations remain expensive and formidable especially for large-scale systems. At present, continuum mechanics models have been regarded as an effective method and widely used to describe the mechanical and physical properties of CNTs [22][23][24][25][26][27].…”

mentioning

confidence: 99%

Wave propagation in carbon nanotubes embedded in an elastic matrix

Dong

Wang

2007

Arch Appl Mech

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This paper reports the results of an investigation into the characteristics of wave propagation in carbon nanotubes embedded in an elastic matrix, based on an exact shell model. Each of the concentric tubes of multi-walled carbon nanotubes is considered as an individual elastic shell and coupled together through the van der Waals forces between two adjacent tubes. The matrix surrounding carbon nanotubes is described as a spring element defined by the Winkler model. The effects of rotatory inertia and elastic matrix on the wave velocity, the critical frequency, and the amplitude ratio between two adjacent tubes are described and discussed through numerical examples. The results obtained show that wave propagation in carbon nanotubes may appear in a critical frequency at which the wave velocity changes suddenly; the elastic matrix surrounding carbon nanotubes debases the critical frequency and the wave velocity, and changes the vibration modes between two adjacent tubes; the rotatory inertia based on an exact shell model obviously influences the wave velocity at some wave modes. Finally, a comparison of dispersion solutions from different shell models is given. The present work may serve as a useful reference for the application and the design of nano-electronic and nano-drive devices, nano-oscillators, and nano-sensors, in which carbon nanotubes act as basic elements.

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Effective bending modulus of carbon nanotubes with rippling deformation

Cited by 54 publications

References 12 publications

Analytical and numerical techniques to predict carbon nanotubes properties

Analytical and numerical techniques to predict carbon nanotubes properties

On the Buckling Behavior of Curved Carbon Nanotubes

Wave propagation in carbon nanotubes embedded in an elastic matrix

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