Material properties emerge from phenomena on scales ranging from angstroms to millimeters, and only a multiscale treatment can provide a complete understanding. Materials researchers must therefore understand fundamental concepts and techniques from vastly different fields. This course is an intensive, 5-day introduction to the fundamentals required to understand state-of-the-art modeling and computer simulation of material behavior with a focus on crystalline materials. Featuring a mix of theoretical lectures, exercises, and hands-on practical computer calculations, the course includes coverage of Continuum Mechanics, Quantum Mechanics, Empirical Interatomic Potentials, Statistical Mechanics, and Spatial Multiscale Methods (e.g. the Quasicontinuum Method). This course includes 40 hours of lectures and recitations, which will be translated into a 2 credit course.
A tentative outline follows:
Day 1 & 2: Sunday & Monday
Introduction to course and computer setup and logistics.
Introduction and Perfect Crystals
Continuum Mechanics and Thermodynamics (CMT)
Day 3 & 4: Tuesday & Wednesday
Quantum Mechanics and Density Functional Theory (DFT)
Classical Atomistics: Molecular Statics (MS)
Day 5 & 6: Thursday & Sunday
Classical Atomistics: MS (continued)
Statistical Mechanics and Molecular Dynamics (MD)
Stress in MD: Continuum laws from atomistic models
Day 7 & 8: Monday & Tuesday
The Finite Element Method (FEM)
Day 9 & 10: Wednesday & Thursday
Multiscale Modeling: Introduction
Multiscale Modeling: Partitioned- Domain Methods
The QC Method: Detailed Formulation of a Static Partitioned-Domain Method
Hands on QC
Tutorials & Homework:
This course covers a broad range of topics. The hands-on exercises are designed to teach key concepts related to practical usage of the computational methods presented in the lectures. Briefly, these are:
- Setting up and running molecular statics simulations with LAMMPS to calculate bulk properties
- Setting up and running molecular dynamics simulations with LAMMPS, to understand thermostats and barostats
- FEM simulation of beams
- QC method simulations of nanobeam bending
Assistance is provided by the two course instructors during the hands-on sessions. Hands-on exercises are completed during the tutorial times and during the mornings/evenings as necessary.
A complete set of lecture slides in PDF format will be provided to all students.