2023/04/22 by Lisa Julia Nebel, Nebel, Lisa Julia, Oliver Sander +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Materials and Mechanics #Cellular Mechanics and Interactions #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2304.11329
openalex publication_date 2023/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate discretizations of a geometrically nonlinear elastic Cosserat shell with nonplanar reference configuration originally introduced by Bîrsan, Ghiba, Martin, and Neff in 2019. The shell model includes curvature terms up to order 5 in the shell thickness, which are crucial to reliably simulate high-curvature deformations such as near-folds or creases. The original model is generalized to shells that are not homeomorphic to a subset of ℝ2. For this, we replace the originally planar parameter domain by an abstract two-dimensional manifold, and verify that the hyperelastic shell energy and three-dimensional reconstruction are invariant under changes of the local coordinate systems. This general approach allows to determine the elastic response for even non-orientable surfaces like the Möbius strip and the Klein bottle. We discretize the model with a geometric finite element method and, using that geometric finite elements are H1-conforming, prove that the discrete shell model has a solution. Numerical tests then show the general performance and versatility of the model and discretization method.