A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: Discretization with geometric finite elements

Research output: Contribution to journalResearch articleContributedpeer-review



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.


Original languageEnglish
Article number116309
Number of pages48
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 31 Aug 2023

External IDs

ORCID /0000-0003-1093-6374/work/142660182
Scopus 85171628987



  • Geometrically nonlinear, Geometric finite elements, Non-orientable, Elastic Cosserat shell, Existence, Nonplanar reference configuration