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

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung



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.


FachzeitschriftComputer Methods in Applied Mechanics and Engineering
PublikationsstatusVeröffentlicht - 31 Aug. 2023

Externe IDs

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



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