The stability and failure mechanism of a structure at the nanometer scale are important for understanding the mechanical behavior of nanoscale materials and structures. This thesis focuses on the material stability of atomic structures. First, the material stability of pristine carbon nanotubes is investigated at the continuum level by using the crystal elasticity theory. A homogenized continuu...

A numerical method called the Boundary Walk Method (BWM) is used to solve problems in two-dimensional potential theory and linear elasticity in multiply connected domains. The BWM is a local method in the sense that it directly gives the solution at the point of interest. It is based on a global integral representation of the unknown function in the form of a potential, followed by evaluating t...

Due to considerable stored energy in surfaces of nano-scales in comparison with the stored energy in their bulk, considering the surface energy is necessary for the analysis of various behaviors of nano-scales for more precise design and manufacturing. In this article, the longitudinal dynamic behavior of nanobars in the presence of the surface energy parameters is studied. To this end, the lon...

Based on the standard finite element method, a new finite element method which is known as nonlocal finite element method (NL-FEM) is numerically implemented in this article to study the nonlocal effects for solving 1D nonlocal elastic problem. An Eringen-type nonlocal elastic model is considered. In this model, the constitutive stress-strain law is expressed interms of integral equation which ...

We present an atomic scale theory of lattice distortions using strain-related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and can describe elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures aroun...

This brief article provides an independent derivation of a formula given by Kafadar and Eringen (1971) connecting two distinct Cosserat spins. The first of these, the logarithmic spin represents the time rate of change of the vector defining finite Cosserat rotation, whereas the second, the instantaneous spin, gives the local angular velocity representing the infinitesimal generator of that rot...

The local elasticity of glasses is known to be inhomogeneous on a microscopic scale compared to that of crystalline materials. Their vibrational spectrum strongly deviates from that expected from Debye's elasticity theory: The density of states deviates from Debye's law, the sound velocity shows a negative dispersion in the boson-peak frequency regime and there is a strong increase of the sound...

Three-dimensional exact solutions for temperature and thermoelastic stresses in multilayered anisotropic plates are derived advanced boundary-value problems with general boundary conditions. The extended Stroh formalism is formulated to include the thermal coupling Eringen nonlocal elasticity theory that captures small scale effects. simply supported structures subjected time-harmonic distribut...