Axial Buckling Behavior of Double-Wall Carbon Nanotubes by Finite Element Simulation

2012 ◽  
Vol 562-564 ◽  
pp. 339-342
Author(s):  
Li Jie Chen ◽  
Yi Fan Zhang ◽  
Qi Zhao
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Aspect Ratio ◽  
Van Der Waals ◽  
Maximum Amplitude ◽  
Van Der Waals Force ◽  
Single Wall Carbon Nanotubes ◽  
Buckling Behavior ◽  
Element Simulation ◽  
Double Wall

With finite element (FE) simulation, we study the buckling behavior of double-wall carbon nanotubes (DWCNTs) under axial compression. In the FE models, linear beam elements and nonlinear spring elements are used to simulate the complex structures and the Van der Waals' force between non-bond atoms from different layers is considered by the Lennard-Jones potential function. The effect of aspect ratio of DWCNTs and double-atoms vacancy on the buckling modes and the critical buckling strains are investigated. The computational results indicate that with the increase of aspect ratio, the critical buckling strains will decrease. For both armchair and zigzag DWCNTs, the critical buckling strains are generally larger than those of the single-wall carbon nanotubes with the same chirality as the external layers and those of the same structures without Van der Waals' force. For defective DWCNTs, the buckling strains of each order decrease by a maximum amplitude of 32.3%.

The Computation of Elastic Constants of Double Wall Carbon Nanotubes Based on the Finite Element Method Considering Van Der Waals' Force

2012 ◽  
Vol 562-564 ◽  
pp. 334-338 ◽  
Author(s):  
Li Jie Chen ◽  
Lin Bo Li ◽  
Qi Zhao
Keyword(s):  
Finite Element Method ◽  
Carbon Nanotubes ◽  
Finite Element ◽  
Aspect Ratio ◽  
Elastic Constants ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Internal Layer ◽  
The Finite Element Method ◽  
Double Wall

Based on the finite element method (FEM), we study the elastic constants of double-wall carbon nanotubes (DWCNTs). In the models, the Lennard-Jones potential function is used to consider the Van der Waals' force between non-bond atoms from different layers. The variations of the elastic constants with the diameter and the aspect ratio of the internal layer nanotube are investigated systematically. The computational results indicate that for both the armchair and the zigzag DWCNTs, the elastic moduli are generally lower than those of the single-wall carbon nanotubes with the same chirality as the internal and external layers. With the increase of the diameter and the aspect ratio of the internal layer carbon nanotubes, the elastic constant of DWCNTs will fall to a stable value.

Vibration Simulations of Double-Walled Carbon Nanotubes by Finite Element Method

2013 ◽  
Vol 774-776 ◽  
pp. 21-24
Author(s):  
Yu Jia ◽  
Li Jie Chen ◽  
Qi Zhao
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Aspect Ratio ◽  
Natural Frequency ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Vacancy Defects ◽  
Vibration Behavior ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Finite element (FE) method is used to study the vibration behavior of armchair and zigzag double-walled carbon nanotubes (DWCNTs). In the analysis, nonlinear spring elements and the Lennard-Jones potential function are used to simulate the Van der Waals' force between non-bond atoms of different tube layers. We systematically analyze the effects of aspect ratio, double-atom vacancy defects and Van der Waals' force on the vibration behavior of DWCNTs. The simulation results show that the first order natural frequency decreases with the increase of length-to-diameter ratio (aspect ratio), the existence of Van der Waals' force causes the increase of natural frequency, and double-atom vacancy defects results in the decrease of each order natural frequency.

Finite Element Modeling of van der Waals Interaction for Elastic Stability of Multi-Walled Carbon Nanotubes

2008 ◽  
Vol 55-57 ◽  
pp. 525-528 ◽  
Author(s):  
Chawis Thongyothee ◽  
Somchai Chucheepsakul
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Van Der Waals ◽  
Compressive Force ◽  
Covalent Bond ◽  
Van Der Waals Force ◽  
Tube Length ◽  
Axial Compressive Force ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

The purpose of this study is to assess the effect of van der Waals interactions within multi-walled carbon nanotubes with the three dimensional finite element models. The elastic buckling behaviors of nanotubes are treated under axial compressive force acting on open both ends of nanotubes and considered with various boundary conditions. The analysis is based on the assumptions that the covalent bond of each wall is represented by an elastic beam element while the van der Waals force of adjacent walls are represented by a nonlinear truss element following the Lennard-Jones “6-12” theory. The models of double-walled carbon nanotubes are used to explain the characteristic of multi-walled carbon nanotubes and then results compared with the column theory. The results show that the critical load of nanotubes depends on atomic arrangement, tube length, and number of walls, while the van der Waals force has a small effect on the buckling load for multi-walled carbon nanotubes.

The Interfacial Cohesive Law of Composite for Carbon Nanotubes and Single Crystal Metals

2012 ◽  
Vol 557-559 ◽  
pp. 505-509
Author(s):  
Gao Feng Wei ◽  
Ting Ting Yan ◽  
Hong Fen Gao
Keyword(s):  
Carbon Nanotubes ◽  
Single Crystal ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Single Wall Carbon Nanotubes ◽  
Cohesive Law ◽  
Crystal Lattices ◽  
Metal Atoms ◽  
Composite Interface ◽  
Analytical Expressions

In this paper the interfacial cohesive law of composite for single-wall carbon nanotubes (CNTs) and single crystal metal is characterized by van der Waals force, and the new interfacial cohesive law is established. The van der Waals force is sensitively related to the distance of atoms, therefore single crystal metal is delaminated according to the structure of crystal lattices that the metal atoms of same distance to CNTs are divided into one layer, and a series of parameters are obtained. The analytical expressions of the new cohesive law are useful to studying the composite interface between CNTs and single crystal metal, and can give the macro properties of the composites accurately.

Effect of van der Waals force on wave propagation in viscoelastic double-walled carbon nanotubes

2018 ◽  
Vol 32 (24) ◽  
pp. 1850291
Author(s):  
Yugang Tang ◽  
Ying Liu
Keyword(s):  
Carbon Nanotubes ◽  
Wave Propagation ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Strain Gradient Theory ◽  
Flexural Wave ◽  
Gradient Theory ◽  
Beam Model ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, the influence of van der Waals force on the wave propagation in viscoelastic double-walled carbon nanotubes (DWCNTs) is investigated. The governing equations of wave motion are derived based on the nonlocal strain gradient theory and double-walled Timoshenko beam model. The effects of viscosity, van der Waals force, as well as size effects on the wave propagation in DWCNTs are clarified. The results show that effects of van der Waals force on waves in inner and outer layers of DWCNTs are different. Flexural wave (FW) in outer layer and shear wave (SW) in inner layer are sensitive to van der Waals force, and display new phenomena. This new finding may provide some useful guidance in the acoustic design of nanostructures with DWCNTs as basic elements.

Superplastic Forming Formula for Aluminum Channel Panels

2005 ◽  
Author(s):  
Frank G. Lee ◽  
M. David Hanna
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Superplastic Forming ◽  
Forming Process ◽  
Taguchi Design Of Experiment ◽  
Forming Parameters ◽  
Physical Experiments ◽  
Element Simulation ◽  
Experiment Method ◽  
Sectional Analysis

A parametric study was conducted to determine how the design features and forming parameters affect part thinning and forming time in the Superplastic Forming Process (SPF). Explicit formulas, describing the maximum percent thinning and the forming time for channel parts formed by the SPF process as a function of eight designs and forming parameters, were derived. The formulas are good approximations of those obtained by finite element simulation analyses and physical experiments. Thinning of the channels was influenced most by the component aspect ratio (height versus width) and entry radius at top of the channel forming tool. The forming time was most influenced by strain rate, aspect ratio and tool bottom radius. A design domain can be established to avoid excessive thinning. The Taguchi design-of-experiment method was applied to select parameter combinations, and the MARC finite element code was used to conduct sectional analysis for various combinations.

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