The students gain knowledge about the different length and time scales on which the phenomena and mechanisms of material behaviour occur. They furthermore understand the different levels of how to describe these phenomena and the existing approaches to bridge and integrate these scales including their range of validity. The students build up the skills to independently develop scale bridging models that integrate all necessary scales and employ these models to describe and predict materials behaviour under given conditions.


  • Characterization of relevant length and times scales in materials science
  • Concepts of concurrent and hierarchical multi-scale approaches
  • Classical homogenization techniques (Taylor/Sachs and Voigt/Reuss)
  • Micromechanical modeling (crystal plasticity, polycrystalline and multiphase materials)
  • Dislocation-based plasticity models
  • Total energy methods in atomistics
  • Atomistic calculation of fundamental physical and material properties
  • Calculation of free energy
  • Basics of the Monte Carlo method
  • Examples and applications of different multiscale methods in the class