Simulation Of Carbon Nanotube Mechanical Behaviors

Nano-materials are considered to be one of the most important materials in the 21th century and they will be the fundamental structures of the intelligent society. The most representative material of nano-materials is carbon nanotube (CNT) which possesses excellent performances in many fields. Ever since Japanese scientist found CNT in 1991, lots of researches have been performed by the scholars all over the world. The research centers on nanomaterials have been found in many contries, including the USA, UK, France, Germany, Japan and China. The behavior and application of CNTs is a key task in these centers. The investigations of single-walled carbon nanotube (SWCNT) have been sellected as the "ten key" scientific achievements together with "Mars PathFinder" all over the world in 1997.CNT possesses excellent mechanical, physical, chemical and electrical properties and it has lots of potential application areas. However there are still many works to be done to get the breakthrough in the engineering applications. Many scientists heve devoted themselves to the investigations of CNT and their research works have been shown to have crucial theoretical and applied values in engineering applications.This dissertation proposes a couple of new analysis methods and applies them in the simulation of the mechanical behaviors of CNTs. The research works are listed as below:1. Simulation of the mechanical behaviors of SWCNT using molecular structural mechanics methodThe molecular structural mechanics method bases on the molecular mechanics method. The inter-atoms covalent bonds are considered as macro-beams. Then the microscopic structures of SWCNTs are equivalently treated as rigid frames in macroscopic structures and solved using structural mechanics method.By now, lots of works have been done by the researchers but they are mainly related to the theoretical analysis for simple problems. In this dissertation, the molecular structural mechanics method is combined with the finite element method and the simulation results of the Young's modulus, shear modulus and dynamic properties of SWCNT using commercial FE software are performed. The results show that the Young's modulus and shear modulus are sensitive to the diameters of SWCNT, i.e. they vary significantly with respect to the nanotube's diameter. Furthermore, for SWCNT, when the damping effect is not considered the fundamental frequency depends on the ratio of the nanotube's length and its diameter. In the end, the contributions of field constants in molecular mechanics method to the mechanical behaviors of SWCNT are discussed.2. Simulation of the mechanical behaviors of SWCNTs using modified molecular structural mechanics methodA modified molecular structural mechanics method, based on molecular mechanics and similar to the finite element method, has been developed in the author's research group for the simulateion of the mechanical behaviors of SWCNTs. The atomic structures of SWCNTs are not simply treated as macro-structures but related to the deformed potential energy using the force-field energy functions. Under the small deformation assumption and the principle of minimum potential energy, the system equation can be established directly from the discretization of the system energy formulation. The inversion potential energy is considered in this formulation which improves the analysis accuracy and widens the analysis fields.Based on the previous work of the author's research group, this dissertation systematically investigates the relationships of the Young's modulus and shear modulus with the diameter of SWCNT and the relationship of fundamental frequency with the ratio of the nanotube's length and its diameter.3. Simulation of the mechanical behaviors of CNTs using the chemical bond element methodAlso based upon molecular mechanics method, a kind of three dimensional (3-D) nano-scale finite element model, the chemical bond element model, is proposed for the simulations of the mechanical properties of SWCNTs. Chemical bonds between carbon atoms are modeled by the chemical bond elements. The constants of the sub-stiffness matrix are determined by using a linkage between the molecular mechanics and continuum mechanics. The entries in the sub-stiffness matrix of the chemical bonds elements are the functions of the force-field constants. The simulations of the mechanical behaviors of CNTs are carried out by means of commercial FE software, ANSYS, after the element stiffness sub-matrix is properly defined. For SWCNT, the relationship of the Young's modulus and shear modulus with the nanotube's diameter and the relationship of fundamental frequency with the ratio of the nanotube's length and its diameter are investigated again by the new method. Furthermore, the simulation of the basic mechanical behaviors of the nanobalance is performed. The fundamental concepts and constitutions of nanobalance are presented and the principle using nanobalance to detect the mass of the attached particle is discussed. The theoretical and numerical solutions in calculating the mass of the attached particle are explored. The impacts of the length, diameter and the location of the attached particle to the resonant frequency of nanobalance are studied and some beneficial advices to enhance the sensitivities of nanobalance are given out. Besides, the effective thickness of SWCNT is proposed by parameter fitting method. In the end, the mechanical behaviors of double-walled carbon nanotube(DWCNT) are simulated where the Van der waals force between the inter-layer atoms is represented by a kind of non-linear spring. Investigations for DWCNT include its Young's modulus and shear modulus and a special vibration mode, i.e. the mode for inter-layer tube when the outer-layer atoms are fixed.