Topics in the Atomistic-to-Continuum Coupling Methods for Material Science

Atomistic-to-continuum coupling methods (a/c methods) have been proposed to increase the computational efficiency of atomistic computations involving the interaction between local crystal defects with long-range elastic fields. This course provides an introduction to the fundamentals required to understand modeling and computer simulation of material behavior. This course will first briefly review material from continuum mechanics, materials science including crystals and defects and then move on to advanced topics in development and analysis of a/c coupling methods both in static and dynamic cases. I will also select topics from statistical mechanics and temporal multiscale accelerated molecular dynamics methods (hyperdynamics, parallel replica dynamics).