Computational homogenization

In Material Mechanics, Computational homogenization is typically used to seek the effective response of a material at a length-scale exceeding that of its underlying microstructure by far. We thus consider problems where it is unfeasible to resolve the actual microstructure in a single analysis at the scale of engineering interest, but where the influence from the microstructure needs to be accounted for explicitly. Important examples are, e.g., engineered composites, poly-crystals and porous media.

Within computational homogenization, two different approaches can be distinguished: (i) Virtual testing, where the effective properties of the material are computed numerically from digital microstructure models replacing macroscopic material testing, and (ii) Finite Element squared (FE²) procedures, where concurrent finite element analyses at two separated length-scales are considered simultaneously in a coupled fashion.

Course content:

• Classic homogenization (linear elasticity)
• Computational homogenization (linear elasticity)
•  FE² for non-linear material modeling
•  FE² for finite deformation hyper-elasticity
•  Effective bounds from virtual testing of random media
•  Variationally consistent homogenization and extension to non-standard applications
• Numerical model reduction 

-         Jänicke, Larsson, Runesson: Computational Homogenization in Material Mechanics (Course compendium) In addition, shorter texts may be distributed in class as well as a more complete list of reference literature.