| The topic of this dissertation is the study of the mechanical properties of solid material systems at the nanoscale. At such length scales, materials can be viewed as particle systems, and molecular dynamics (MD) simulations help one understand their behavior as well as quantify their properties. However, mechanical concepts such as strain, stress and moduli were originally developed in continuum models, which are typically applied in space scales that range from the microscopic to the macroscopic. For this reason, a careful translation of ideas from continuum scales to the nanoscale is necessary.; In essence, this thesis reviews and refines the continuum notions of average mechanical properties, such as stress and strain, and the meaning of such notions when MD is used to compute them. A Lagrangian-based approach is utilized for the purpose of determining the stress-deformation behavior of continua as well as of particle systems. At the continuum level, the mentioned Lagrangian-based approach is applied within homogenization theory for developing a nonlinear continuum homogenization model, which includes a novel constitutive relation for the stress. At the nanoscale, an MD method is presented as the extension of the continuum homogenization model. This MD method is able to simulate the behavior of particle systems under a given type of deformation as well as to generate stress-strain curves. In the process of developing the MD method, some concepts and techniques commonly used in MD, such as the virial stress and the Parrinello-Rahman method, are clarified. |
