Dominic Zäh

Homogenization and Multiscaling of Granular Media for Different Microscopic Constraints

We outline a method for quasi-static homogenization of granular microstructures and its embedding into two-scale simulations. A consistent extension of classical stiff, soft and periodic boundary conditions from continuous to granular microstructures induces new classes of micro-to-macro transitions for granular aggregates. These boundary conditions include constraints not only for particle center displacements but also for particle rotations at a driving boundary frame. The stiff and soft constraints at the driving frame of the particle aggregate induce upper and lower bounds of the particle aggregate stiffness. We outline a unified implementation of the displacement- and rotational constraints by penalty methods that proves to be convenient for straightforward integration into discrete element codes. Finally, we embed granular microstructures into a coarse graining discrete-to-finite element model, where they govern the micromechanical behavior of a two-scale simulation.