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We investigate discretizations of a geometrically nonlinear elastic Cosseratshell with nonplanar reference configuration originally introduced by B\^irsan,Ghiba, Martin, and Neff in 2019. The shell model includes curvature terms up toorder 5 in the shell thickness, which are crucial to reliably simulatehigh-curvature deformations such as near-folds or creases. The original modelis generalized to shells that are not homeomorphic to a subset of$\mathbb{R}^2$. For this, we replace the originally planar parameter domain byan abstract two-dimensional manifold, and verify that the hyperelastic shellenergy and three-dimensional reconstruction are invariant under changes of thelocal coordinate systems. This general approach allows to determine the elasticresponse for even non-orientable surfaces like the M\"obius strip and the Kleinbottle. We discretize the model with a geometric finite element method and,using that geometric finite elements are $H^1$-conforming, prove that thediscrete shell model has a solution. Numerical tests then show the generalperformance and versatility of the model and discretization method.

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