Multiscale Mechanics of Materials (440620-WS 24/25)

Course Description:

Mechanical deformation of structural materials is a multiscale phenomenon, with processes taking place at many different time- and length-scales. Modern computational modelling of materials requires mechanism-based descriptions of these processes, to be able to suggest new engineering strategies. In this course, students will gain a fundamental understanding of the multiscale nature of the mechanical behaviour of materials and of the different approaches to take this into account in mechanical modelling of microstructures. They will identify the relevant length- and timescales of the microscopic processes that lead to meso- and macroscopic structure-property relationships. Students will learn about the principles of effective theory construction, coarse graining and homogenisation methods, and how to apply these methods to identify, analyse and model multiscale problems, such as plastic deformation, work hardening and strength of microstructures. Through the lectures and hands-on exercises, students will become familiar with state of the art numerical and theoretical scale-bridging modelling methods. In the end, they are able to apply numerical tools on different length scales, and understand the underlying principles (ab-initio electronic structure calculations, atomistic modelling, discrete dislocation dynamics, crystal and continuum plasticity).

Content:

• Introduction to problems in materials mechanics that involve multiple length and time scales.

• Overview over concepts of concurrent and hierarchical multiscale modeling of materials.

• Principles of effective theory construction and its realisability in numerical modeling (extracting and passing information in hierarchical models); coarse graining and homogenization.

• Bridging scales in elasticity, plasticity and fracture modeling
  

• Numerical models and technical aspects of hierarchical multiscale simulations (ab-initio electronic structure calculations, atomistic modeling, discrete dislocation dynamics, continuum and crystal plasticity).