Nano Mechanics and Multiscale Modelling
Nanomekanik och flerskalig modellering

FMEN25F, 7.5 credits

Valid from: Autumn 2018
Decided by: Anders Gustafsson
Date of establishment: 2018-10-24

General Information

Division: Mechanics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMEN25
Teaching language: English

Aim

Material properties emerge from phenomena on scales ranging from angstroms to meters. A multiscale treatment can provide a basis for an understanding of material behavior on different scales. The course addresses advanced undergraduate and graduate students. The purpose of the course is to present the theories and methods in multiscale modeling of materials and establish relations between atomistic descriptions and continuum mechanics. The course gives basic knowledge about the principles, concepts and methods in nanomechanics based on Euler-Langrange’s, Hamilton’s and Schrödinger’s formulations of the mechanical laws. The general concepts and principles are presented and combined with interatomic potential functions for different materials. The course further involves the basics of classical statistical mechanics and quantum mechanics and provides a framework for further studies in molecular dynamics.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• Acquire knowledge of the hierarchy of physical models
• apply the fundamental equations – Euler-Lagrange, Hamilton and Schrödinger
• explain and apply fundamental interatomistic potential functions
• acquire knowledge of the most important principals of molecular dynamics
• acquire knowledge about the relation between classical statistical mechanics, quantum mechanics and continuum mechanics.

Competences and Skills

For a passing grade the doctoral student must

• Identify relevant interatomistic potential functions for analysis of material systems
• be able to formulate and numerically solve simple problems in molecular dynamics
• be able to perform an analysis of a nanomechanical problem and to present the results in a well-written report

Judgement and Approach

For a passing grade the doctoral student must

• Adopt a critical and innovative attitude towards multiscale modelling
• be able to evaluate achieved results based on problem formulation and physical limitations

Course Contents

Introduction of hierarchy of physical models of materials. Fundamental continuum mechanics and thermodynamics. Lattices and crystal structures. Quantum mechanics. Empirical atomistic models of materials. Molecular statics. Atomistic foundations of continuum concepts: classical equilibrium, statistical mechanics, microscopic expressions for continuum fields, molecular dynamics. Multiscale methods: multi scale modelling, atomistic constitutive relations for multi lattice crystals, atomistic-continuum coupling: static methods, non-zero temperature and dynamics. Overview of fabrication techniques for today's nanostructures and modern experimental methods at the nano scale.

Course Literature

Tadmor, Ellad B. & Miller, Ronald E.: Modeling Materials: Continuum, Atomistic and Multiscale Techniques. Cambridge University Press, 2011. ISBN 9780521856980.

Instruction Details

Types of instruction: Lectures, exercises, project

Examination Details

Examination formats: Written exam, written report
Grading scale: Failed, pass
Examiner:

Admission Details

Course Occasion Information

Contact and Other Information

Course coordinators: