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Petr Henyš (TUL): Homogenization and multi-scale modeling with arbitrary finite element meshes

17 Apr 2019   10:00-11:00

Periodic boundary conditions (PBCs) are often used to estimate the homogenized properties of a media using the finite element method (FEM). The optimal treatment of PBCs requires the finite element mesh to be conformal on the boundaries where the PBCs are prescribed. Nevertheless, it is difficult to enforce PBCs on complex geometrical domains with multiple material phases with current finite element meshing algorithms. This study focuses on the treatment of PBCs on arbitrary meshes without conformal boundaries. The presented method for treatment of PBCs is based on the Nitsche's method, which allows imposing Dirichlet boundary conditions weakly as well as interface contact constraints. The proposed method is tested and compared with the state-of-the-art methods (mortar and meshless methods) within a set of numerical benchmarks. The resultant homogenized properties differ up to 1 % and can be considered negligible, while the Nitsche's method does not increase the size of the model and does not require manual tuning of additional parameters, unlike the meshless method.

B-366, Faculty of Civil Engineering, Thákurova 7, 166 29 Prague 6
Contact person
Jan Zeman, jan.zeman@cvut.cz
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