The response of single crystals to increasing shock strength involves complex phase
transition processes from solid-solid to solid-liquid phases. However, it is not yet fully …

We present an efficient a posteriori error control strategy for an energy-based concurrent
multiscale method with sharp interface in molecular mechanics, namely the geometric …

Despite their success in microscale modeling of materials, atomistic methods are still limited
by short time scales, small domain sizes, and high strain rates. Multiscale formulations can …

Adaptive atomistic/continuum (a/c) coupling method is an important method for the
simulation of material and atomistic systems with defects to achieve the balance of accuracy …

This work introduces a theoretical formulation and develops numerical methods for finite
element implementation of the formulation so as to extend the concurrent atomistic …

Coupled atomistic–continuum methods can describe large domains and model dynamic
material behavior for a much lower computational cost than traditional atomistic techniques …

This dissertation is broadly divided into four primary topics which build upon each other and
represent the main projects I worked on during my PhD. Furthermore, this work resulted in …