Finite Element Modeling of Nanotube Structures (eBook)

Preface 7
Acknowledgments 8
Contents 9
1 Nanotubes 12
1.1 Introduction 12
1.2 Carbon Nanotubes 13
1.3 Atomic Structure and Morphology of CNTs 13
1.4 Inorganic Nanotubes 18
1.5 Mechanical Properties of Nanotubes 18
References 23
2 Interatomic Bonding 25
2.1 Potential Energy Function (PEF) 25
2.2 Harmonic Functions for Carbon Nanotubes 28
2.3 Morse Potential Functions for CNTs 29
2.4 Potential Interactions for Inorganic Nanotubes 31
2.4.1 Long Range Interactions 32
2.4.2 Short Range Interactions 33
References 34
3 Finite Element Modeling of Nanotubes 36
3.1 Geometry and Structure of Nanotubes 36
3.1.1 Modeling of CNTs with Specific Chirality 40
3.1.2 Geometries of Multi-walled Carbon Nanotubes 42
3.1.3 Geometry of Inorganic Nanotubes 42
3.2 Modeling the Mechanical Properties of Carbon Nanotubes 45
3.2.1 Analytic Solution 47
3.2.2 Computing Some Mechanical Properties of Carbon Nanotubes 49
3.3 Modeling the Mechanical Properties of Inorganic Nanotubes 50
References 55
4 Nanotube Modeling Using Beam Element 56
4.1 Introduction 56
4.2 Forces Between Bonds in Nanotubes 58
4.3 Beam and Frame Elements 62
4.3.1 Three-Dimensional Beam Element 66
References 69
5 Linear Finite Element Analysis of Nanotubes 71
5.1 Introduction 71
5.2 Overview of ANSYS Software 76
5.3 Building a Linear Model for a Typical SWCNT 76
5.3.1 Specifying Units 77
5.3.2 Defining Element Types and Real Constants 78
5.3.3 Defining Material Properties 78
5.3.4 Defining the Cross Section of the Element 81
5.3.5 Creating Carbon Nanotube Model 83
5.3.6 Creating Inorganic Nanotube Model 84
5.3.7 Meshing the Generated Nanotube 89
5.3.8 Boundary Conditions 92
5.3.9 Initiation of Solution for Nanotube Model 96
5.3.10 Post Processing 97
5.3.11 Element Table 102
5.4 Simulating Other Mechanical Behaviors for Nanotubes 106
5.4.1 Buckling Behavior 109
5.4.2 Bending Behavior 110
5.4.3 Torsional Behavior 110
5.4.4 Modal Behavior 112
References 112
6 Non-linear Finite Element Analysis of Nanotubes 115
6.1 Introduction 115
6.2 Non-linear Simulation of Carbon Nanotube 117
6.2.1 Problem Description 117
6.2.2 Defining Element Type 118
6.2.3 Defining Material Properties 118
6.2.4 Defining the Element Cross Section 121
6.2.5 Creating the Nanotube Geometry 121
6.2.6 Boundary Conditions and Loads 122
6.2.7 Non-linear Solution 128
6.2.7.1 Curves and Legend 130
6.2.8 Post Processing 132
6.2.9 Stress-Strain Curve of the Nanotube 134
6.3 Non-linear Simulation of Inorganic Nanotubes 138
References 139
7 Effect of Geometrical Parameters on Tensile Properties of Nanotubes 140
7.1 Introduction 140
7.2 Effect of Nanotube Length on its Mechanical Behavior 141
7.3 Effect of Wall Curvature on Strength of CNTs 144
7.4 Effect of Chirality on Strength of CNTs 150
7.5 Effect of Geometric Parameters on the Mechanical Behaviors of Inorganic Nanotubes 153
7.6 Convergence and Mesh Independence Study 157
References 160
8 Finite Element Analysis of Multi-walled Nanotubes 163
8.1 Introduction 163
8.2 Modeling Multi-walled Carbon Nanotubes 163
8.3 Tensile Behavior of MWCNT 167
References 169
9 Influence of Defects on the Strength of Graphene and Carbon Nanotube 170
9.1 Introduction 170
9.2 Problem Description 172
9.3 Modeling of Defective CNT and Graphene Structures 172
9.4 Post Processing for Defective CNT and Graphene 174
References 178
10 Mechanical Behavior of Carbon Nanotube-Reinforced Polymer Composites 179
10.1 Introduction 179
10.2 Computational Modeling of CNT Based Composites 180
10.3 Modeling Procedure for RVE 182
10.3.1 Polymer Matrix 184
10.3.2 CNT Polymer Interaction 185
10.3.3 Boundary Conditions and Assumptions for RVE 185
10.3.3.1 CNT Through the Length of the RVE 186
10.3.3.2 CNT Inside the RVE 187
10.4 Tensile Loading of the RVEs 188
10.4.1 Effect of CNT Length on the Modulus of CNT/PP Composites 189
10.4.2 Effect of Interface on the Modulus of CNT/PP Composites 201
References 214