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Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMEN25F valid from Autumn 2018

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General
  • English
  • Once every semester
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.
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.

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
Types of Instruction
  • Lectures
  • Exercises
  • Project
Examination Formats
  • Written exam
  • Written report
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
Selection Criteria
Literature
  • Tadmor, Ellad B. & Miller, Ronald E.: Modeling Materials: Continuum, Atomistic and Multiscale Techniques. Cambridge University Press, 2011. ISBN 9780521856980.
Further Information
Course code
  • FMEN25F
Administrative Information
  • 2018-10-24
  • Anders Gustafsson

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