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We consider a recently introduced geometrically nonlinear elastic Cosseratshell model incorporating effects up to order $O(h^5)$ in the shell thickness$h$. We develop the corresponding geometrically nonlinear constrained Cosseratshell model, we show the existence of minimizers for the $O(h^5)$ and $O(h^3)$case and we draw some connections to existing models and classical shell strainmeasures. Notably, the role of the appearing new bending tensor is highlightedand investigated with respect to an invariance condition of Acharya [Int. J.Solids and Struct., 2000] which will be further strengthened.

journal of elasticity

A constrained Cosserat shell model up to order $O(h^5)$: Modelling,  existence of minimizers, relations to classical shell models and scaling  invariance of the bending tensor