Study Of Related Mechanical Problems For Carbon Nanotubes

Since their discovery by Iijima, carbon nantoubes (CNTs) have attracted much attention and interest from scientists in various disciplines. Many studies show that CNTs possess possibly unique mechanical, electronical and optical properties which result in potential applications in industry. However, both of experimental and theoretical works for CNTs have been being in a groping stage, and there are still some significant discrepancies among the results of mechanical properties of CNTs. Thus, based on the higher-order Cauchy-Born constitutive model and the generalized parametric constitutive law for van der Waals force developed here, a series of mechanical properties, compression buckling and adhesion behaviors for single-walled carbon nanotubes (SWCNTs) are studied respectively in the present thesis. The following progresses are made:Based on the higher order Cauchy-Born rule, a constitutive model of SWCNT is established. In the present model, by including the second order deformation gradient tensor in the kinematic description, the limitation of the standard Cauchy-Born rule for the modeling of nanoscale crystalline films can be alleviated with less computational efforts. Based on the established relationship between the atomic potential and the macroscopic continuum strain energy density, analytical expressions for the tangent modulus tensors are derived. Moreover, the interatomic potential and the atomic structure of CNT are incorporated into the proposed constitutive model in a consistent way. Therefore SWCNT can be viewed as a macroscopic generalized continuum with microstructure.Based on the higher-order Cauchy-Born constitutive model, a seriers of infinitesimal mechanical properties and the strain energy for the graphite sheet and SWCNT are studied firstly with the consideration of the influences from tube chirality and radius, potential parameters and the inner displacement. The results show that infinitesimal properties of SWCNTs strongly depends on the tube radius as for smaller tubes, however, the dependence becomes very weak as for larger tubes and a plateau, which corresponds to the modulus of graphite predicted by the present method, is reached with increase of tube radius. It is also noted that potential parameters and the inner displacement have significant influences on mechanical properties of SWCNTs. Besides, the strain energy and the tangential elastic moduli for CNTs are also obtained under finite deformation. The results show that the tangential elasitic moduli decreases linearly with increasing the axial stretch, and the strain energy for SWCNTs with similar tube radius is consistent with each other. Then, the axial-deformation-induced circular and torsion response in chiral SWCNTs is analyzed systematically, and the maximum coupling response is obtained in SWCNT with chiral angle ofπ/12.Some basic problems on the study of the bending stiffness of CNTs are analyzed based on their defomation mechanism. It is pointed out that the bending stiffness of a flat graphite sheet and that of CNTs are two different concepts. The former is an intrinsic material property while the later is a structural one. Since the smeared-out model of CNTs is a generalized continuum with microstructure, its effective bending stiffness should be regarded as an independent structural rigidity parameter which can not be determined simply by employing the classic formula in beam theory. Furthermore, based on the higher-order Cauchy-Born constitutive model, the reasonable computational methods and results for the bending stiffness of the graphite sheet and CNTs are given.Based on the higher-order Cauchy-Born constitutive model, the compression deformation beyond the buckling point for SWCNTs is implemented numerically via the mesh-free method, and is analyzed based on the strain energy obtained. Results consistent with those based on molecular dynamic and atomic finite element methods confirm the feasibility and validity of the presented constitutive model.A parametric variational principle for van der Waals force simulation between any two non-bonded atoms is also established together with the corresponding improved quadratic programming method for numerical simulation of mechanical behaviours of carbon nanotubes. Carbon-carbon covalent bond interaction in carbon nanotubes is modeled and computed based on molecular structural mechanics model. Van der Waals force is simulated by the network of bars with a special nonlinear mechanical constitutive law in the finite element analysis. In comparison with conventional numerical methods, the suggested method does not depend on displacement and stress iteration, but on the base exchanges in the solution of a standard quadratic programming problem. Thus, the model and method developed exhibit very good convergence behavior in computation and provide accurate predictions of the mechanical behaviours and displacement distributions in the nanotubes. Based on the present method, the equilibrium configuration and the adhesion behaviors for two parallel or cross SWCNTs are studied respectively. Numerical results demonstrate the validity and the efficiency of the proposed method.