Christoph Smoch:
Two-scale finite element approximation of a homogenized plate model
Zeit und Ort
Dienstag, 30.4.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Zusammenfassung
We study the discretization of a homogenized and dimension reduced model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Velčić in 2014. Thereby, a nonlinear bending energy is based on a homogenized quadratic form which acts on the second fundamental form associated with the elastic deformation. Convergence is proven for a multi-affine finite element discretization of the involved three-dimensional microscopic cell problems and a discrete Kirchhoff triangle discretization of the two-dimensional isometry-constrained macroscopic problem. Finally, the convergence properties are numerically verified in selected test cases and qualitatively compared with deformation experiments for microstructured sheets of paper.