A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: Discretization with geometric finite elements
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
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 R 2. 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 H 1-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.
Details
Original language | English |
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Article number | 116309 |
Number of pages | 48 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 416 |
Publication status | Published - 31 Aug 2023 |
Peer-reviewed | Yes |
External IDs
ORCID | /0000-0003-1093-6374/work/142660182 |
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Scopus | 85171628987 |
Keywords
Keywords
- Geometrically nonlinear, Geometric finite elements, Non-orientable, Elastic Cosserat shell, Existence, Nonplanar reference configuration