The discovery of carbon nanotubes (CNTs) in 1991 by Iijima revealed the possibility of ultra-strong materials exploiting the properties of materials at smaller length scales. The superior strength, stiffness, and ability to perform under extreme conditions motivated researchers to investigate further on CNTs and similar materials at nanoscale. This resulted in discovery of various nanostructures such boron nitride nanotubes (BNNTs), graphene, hexagonal boron nitride sheets etc. Many of such nanostructures exhibited superior strength and stiffness comparable to that of CNTs. Out of these nanotubes, BNNTs have recently attracted attention from researchers due to their excellent mechanical properties similar to that of CNTs along with better chemical and thermal stability. Thus, BNNTs can be used for varieties of applications such as protective shield for nanomaterials, optoelectronics, bio-medical, nano spintronics, field-emission tips in scanning tunneling and atomic force microscope, and as reinforcement in composites. BNNTs are also used in other applications such as water cleansing, hydrogen storage, and gas accumulators. To exploit these ultra-strong materials, the mechanics of materials under different conditions of loading and failure need to be studied and understood. Also, to make use of the material in a nanocomposite or other applications, the material properties should be evaluated. The present work is focused on the computational study of the mechanics of nanotubes with special reference to BNNTs and CNTs. Note that the attention is not given to the material but to the nanostructure and mechanics. Hence depending on the state-of-the-art, BNNTs and CNTs are used wherever it is appropriate along with justifications. The chapter-wise outline of the present work is given below. The first chapter is an introduction along with a state-of-the-art literature review. The second chapter introduces the molecular simulation methodology in brief. The chapters from the third to the seventh present the work in detail and describe the major contributions. The final chapter summarizes the work along with a few possible directions to extend the present work. Chapter 1 In this chapter, the importance of computational techniques to study the mechanics at the nanoscale is outlined. A brief introduction to various nanostructures and nanotubes are also given. A detailed literature review on the mechanics of nanotubes with special attention to elastic properties, buckling, tensile failure, and as reinforcement in nanocomposites is presented. Chapter 2 In this chapter, the molecular simulation technique is outlined. The molecular dynamics (MD) simulation is one of the most common simulation techniques used to study materials at the nanoscale. A few interatomic potentials that are used in an MD simulation are explained. Theories linking continuum mechanics with the molecular dynamics are also explained here. Chapter 3 In this chapter, the elastic behavior of single-walled BNNTs under axial and torsional loading is studied. Molecular dynamics (MD) simulation is carried out with a tersoff potential for modeling the interatomic interactions. Different chiral configurations with similar diameter are considered to study the effect of chirality on the elastic and shear moduli. Furthermore, the effects of tube length on elastic modulus are also studied by considering different aspects ratios. It is observed that both elastic and shear moduli depend on the chirality of a nanotube. For aspect ratios less than 15, the elastic modulus reduces monotonically with an increase in the chiral angle. For chiral nanotubes the torsional response shows a dependence on the direction of loading. The difference between the shear moduli against and along the chiral twist directions is maximum for a chiral angle of 15◦, and zero for zigzag (0◦) and armchair (30◦) configurations. Chapter 4 Buckling of nanotubes have been studied using many methods such as MD, molecular mechanics, and continuum based shell theories. In MD, motion of the individual atoms are tracked under an applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell-theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that a direct application of shell theories to study nanotube buckling often leads to erroneous results. In this chapter, the nonlocal effect on the mechanics of nanostructures is studied using Eringen’s nonlocal elasticity. The buckling of carbon nanotubes is considered as an example to demonstrate and understand the nonlocal effect in the nanotubes. Single-walled armchair nanotubes with the radius varying from 3.4nm to 17.7nm are considered and their critical buckling stresses are predicted based on multiscale modeling techniques including classical and nonlocal continuum mechanics theories and MD simulation. Fitting nonlocal mechanics models to MD simulation yields a radius-dependent length-scale parameter, which increases approximately linearly with the radius of carbon nanotube. In addition, the nonlocal shell model is found to be a better continuum model than the nonlocal beam model due to its ability to include the circumferential nonlocal effect. Chapter 5 In this chapter, the effects of geometrical imperfections on the buckling of nanotubes are studied. The present study reveals that a major source of the error in continuum shell theories in calculating the buckling stress can be attributed to the geometrical imperfections. Here, geometrical imperfections refer to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work the nanotube is modeled as a thin-shell with initial imperfection. Then a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this turn out to be a robust method for a continuum analysis of nanotubes taking in the effect of variation of temperature as well. Chapter 6 In this chapter, the effects of Stone-Wales (SW) and vacancy defects on the failure behavior of BNNTs under tension are investigated using MD simulations. The Tersoff-Brenner potential is used to model the atomic interaction and the temperature is maintained close to 300 K. The effect of a SW defect is studied by determining the failure strength and failure mechanism of nanotubes with different radii. In the case of a vacancy defect, the effect of an N-vacancy and a B-vacancy is studied separately. Nanotubes with different chirality but similar diameter are considered first to evaluate the chirality dependence. The variation of failure strength with the radius is then studied by considering nanotubes of different diameter but same chirality. It is observed that the armchair BNNTs are extremely sensitive to defects, whereas the zigzag configurations are the least sensitive. In the case of pristine BNNTs, both armchair and zigzag nanotubes undergo brittle failure, whereas in the case of defective BNNTs only the zigzag ones undergo brittle failure. An interesting defect-induced plastic behavior is observed in defective armchair BNNTs. For this nanotube, the presence of a defect triggers mechanical relaxation by bond breaking along the closest zigzag helical path, with the defect as the nucleus. This mechanism results in a plastic failure. Chapter 7 In this chapter, the utility of BNNTs as reinforcement for nanocomposites with metal matrix is studied using MD simulation. Due to the light weight, aluminium is used as the matrix. The influence of number of walls on the strength and stiffness of the nanocomposite is studied using single-and double-walled BNNTs. The three body tersoff potential is used to model the atomic interactions in BNNTs, while the embedded atom method (EAM) potential is used to model the aluminium matrix. The van der Waals interaction between different groups — the aluminium matrix with the nanotube or the between the concentric tubes in double walled BNNT — is modeled using a Lennard Jones potential. A representative volume element approach is used to model the nanocomposite. The constitutive relations for the nanocomposite is also proposed wherein the elastic constants are obtained using the MD simulation. The nanocomposite with reinforcement shows improved axial stiffness and strength. The double-walled BNNT provides more strength to the nanocomposite than the single-walled BNNT. The BNNT reinforcement can be used to design nanocomposites with varying strength depending on the direction of the applied stress. Chapter 8 The summary of the work with a broad outlook is presented in this chapter. The major conclusions of the work are reiterated and possible directions for taking the work further ahead are mentioned.