Homogenization and multiscaling of granular media for different microscopic constraints. (English) Zbl 1323.74068
de Borst, René (ed.) et al., Multiscale methods in computational mechanics. Progress and accomplishments. Selected papers based on the presentations at the international colloquium (MMCM 2009), Rolduc, The Netherlands, March 11–13, 2009. New York, NY: Springer (ISBN 978-90-481-9808-5/hbk; 978-94-007-3386-2/pbk; 978-90-481-9809-2/ebook). Lecture Notes in Applied and Computational Mechanics 55, 155-177 (2011).
Summary: 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.
For the entire collection see [Zbl 1202.74012].
For the entire collection see [Zbl 1202.74012].
MSC:
| 74Q10 | Homogenization and oscillations in dynamical problems of solid mechanics |
| 74E20 | Granularity |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
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