Materials Modeling and Simulation

Program Director

Prof. H.C. Öttinger

Introduction

Material properties can be modeled on various length and time scales, ranging from nanometers to meters and from femtoseconds to minutes or even hours. Multiscale modeling is the key to the deepest possible understanding of materials, and bridging scales is a major challenge in current materials science. Computer simulations are the principal tool for treating systems of practical importance. It has been a major breakthrough in materials science and engineering that the computer now offers help in reducing experimental efforts, for example through the calculation of phase diagrams for multicomponent systems or through full processing simulations, and in obtaining theoretical estimates for many materials properties, often leading to deeper understanding.

Objective of Courses

The program is designed to give a flavour of the wide range of possibilities in the theoretical understanding of materials, with an emphasis on bridging scales and computational materials science. All courses are closely related to ongoing research activities.

A fundamental and broad introduction to computer simulations is offered in the course "Introduction to Computational Physics." The advanced course on "Computational Polymer Physics" is a direct continuation in which a number of topics are covered in much greater depth. Students with a general background in computational science and simulations should consider to take the more advanced course directly. A very broad introduction to the foundations and applications of the finite element method is offered in the course "Computer Applications: Finite Elements in Solids and Structures". All courses in computational materials science include programming exercises.

The course "Deformation and Failure of Solids and Liquids" introduces theoretical concepts of modern materials modeling in the particular context of deformation and flow. Statistical nonequilibrium physics, which is the basis for the general theme of bridging scales in materials science, is covered in a series of the two advanced courses "Nonequilibrium Systems" and "Nonequilibrium Statistical Mechanics," where the second of these courses requires the knowledge of the first course on the phenomenological approach to nonequilibrium systems.

Teaching Goals

The courses aim at a thorough understanding of the following topics:

• thermodynamically consistent description of nonequilibrium systems,
• systematic procedures for coarse-graining,
• various ideas of multiscale modeling,
• use of computer simulation techniques (Monte Carlo, molecular dynamics, Brownian dynamics, finite elements, finite differences, multigrid methods, cellular automata, lattice Boltzmann),
• selected theoretical concepts.

Courses

Fall semester
Introduction to Computational Physics
Multiscale modeling and computation
Nonequilibrium Systems
Spring semester
Computational Polymer Physics
Computer Applications: Finite Elements in Solids and Structures
Nonequilibrium Statistical Mechanics