Carbon nanotubes (CNTs) have record high tensile strength and Young’s modulus, which makes them ideal for making super strong yarns, ropes, fillers for composites, solid lubricants, etc. The mechanical properties of CNT bundles have been addressed in a number of experimental and theoretical studies. The development of efficient computational methods for solving this problem is an important step in the design of new CNT-based materials. In the present study, an atomistic chain model is proposed to analyze the mechanical response of CNT bundles under plane strain conditions. The model takes into account the tensile and bending rigidity of the CNT wall, as well as the van der Waals interactions between walls. Due to the discrete character of the model, it is able to describe large curvature of the CNT wall and the fracture of the walls at very high pressures, where both of these problems are difficult to address in frame of continuum mechanics models. As an example, equilibrium structures of CNT crystal under biaxial, strain controlled loading are obtained and their thermal stability is analyzed. The obtained results agree well with previously reported data. In addition, a new equilibrium structure with four SNTs in a translational cell is reported. The model offered here can be applied with great efficiency to the analysis of the mechanical properties of CNT bundles composed of single-walled or multi-walled CNTs under plane strain conditions due to considerable reduction in the number of degrees of freedom.

The distributed lateral load on a plate located in a gas medium has been determined. The difference in the gas pressures of the plate surfaces results in a pressure drop and a lateral force, which depends on the middle surface curvature. It is shown that both these components of the lateral force must be taken into account in the general case. The influence of the second load component is small at a small ratio of the average pressure to the elastic modulus of the plate material and at a large relative thickness of the plate. At a small relative plate thickness and a large ratio of the average pressure of the medium to the elastic modulus of the plate material, the influence of the second component of the lateral load on the bending becomes significant. Cases of both linear and nonlinear plate bending are considered.

The radial dynamics of a single-walled zigzag carbon nanotube under pulsed pressure is studied. Uniform external pressure is applied instantly, then remains constant for a certain time, and then is instantly released. This loading scheme allows one to consider a carbon nanotube under plane strain conditions and replace it with a circular ring formed by one zigzag row of carbon atoms. The bending deformation of the ring in its plane is described by an equation based on the Kirchhoffs hypothesis. An effective parameter is used, including the bending stiffness of the ring and areal density. The regimes of oscillatory motion and exponential growth of radial displacements are investigated depending on the magnitude and duration of the applied pressure. Alternatively, the ring is analyzed in terms of a molecular dynamics model with a reduced number of degrees of freedom, taking into account the plane strain conditions. With the help of molecular dynamics, the limits of the thin shell theory are established. For (n, 0) CNTs with n > 15, in the regime of small-amplitude vibrations, the discrepancy between the continuum model and molecular dynamics calculations does not exceed 5% and decreases with increasing n.

Static cylindrical bending of nanofilms is considered in linear and nonlinear formulations. The frequency spectrum of bending vibrations and the parametric resonance are determined. In this...

The coordinate of a notch and its depth and length are found from three eigenfrequencies of bending vibrations. The notch is a model of a flaw in a bar, in particular, of a transverse open crack. Taking into account that the crack propagates from a small nucleus and not necessarily from the most stressed cross section, it is assumed that the notch can be at any place in the bar.