Some Mechanical Behavors Of One-dimensional Nanostuctures

One-dimensional nanostructures are a huge family of nanomaterials, which have been widely used in the nanotechnology. The study of one-dimensional structures'mechanical behaviors is significantly important in understanding their intrinsic stiffness and strength properties as well as their reliability, durability, and stability in the service process. Thus, some representive one-dimensional structures are considered in this thesis, such as the nanotube, nanowire, and nanoribbon. This research can provide reference for their structural characteristics and also some help in designing related nanodevices. Altogether four kinds of mechanical behaviors are addressed in this thesis, and both analytical and numerical analyses are presented.First, an exact continuum elastica model is proposed to study the peeling process of carbon nanotubes from rigid smooth substrates. It has been found that the van der Waals interaction between the tube and the substrate is related to the tube's vertical displacement as well as the bending angle. Numerical simulations reveal that the peeling process is complex, and sometimes includes sudden transitions between different geometric configurations of the nanotube and equilibrium path branch- switching phenomena. The bending angle plays an important part on the peeling force when the tube's radius and the rotation angle in the adhesion region are both large.Then the flexural wave propagation behavior of nanotubes is addressed. With establishing a new beam model and adopting the strain gradient elasticity theory, factors such as the shear deformation and size effects, which significantly influence the characteristics of waves with short wavelengths, are focused and discussed. It is found that for high wave number cases the frequently used Euler and Timoshenko beam models would fail, and only the present beam model can predict proper results. The wave dispersion curves obtained from the second and fourth order strain gradient theories are inversed U-shaped and N-shaped, respectively. It is demonstrated that the former theory is unstable while the latter one can predict exact results for waves of quite short wavelengths. In addition, the maximum phase velocity usually occurs for nanotubes with inner-outer radius ratio as 0.3, in contrast with 0 predicted by the Timoshenko model.Furthermore, a continuum elastic model for studying weak interfaces of the core-shell nanowires is established. A new beam model is proposed, which vanishes the surface shear stress and satisfies the interfacial cohesive law automatically. Critical buckling loads and resonant frequencies of simply supported nanowires are obtained by using the Ritz method. Numerical examples indicate that the weak interface's effect reduces the overall structural stiffness, which is most significant when the inner-outer radius ratio of the shell is near 0.65. It is also found that the shear deformation and weak interface's effects only need consideration when the nanowire is not quite long, and they affect buckling behaviors more significantly than vibration characteristics.At last, the reported curling morphologies of graphene nanoribbons are studied by continuum modeling. Analytical solutions indicate that the curled shape is determined by the sign of the edge stress, that is, positive value would induce wheel mode while negative one leads to saddle mode. The critical edge stress is found to be inversely proportional to the graphene nanoribbon's width. In addition, the warping deflection of the curled mode can be represented by a quadratic function in the initially curling stage. However, for nanoribbon which is wide or curled severely, this warping deformation would decay quickly near the edges, which should be studied by the exact analysis.