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

Abstract

We consider a recently introduced geometrically nonlinear elastic Cosserat shell model incorporating effects up to order $O(h^5)$ in the shell thickness $h$. We develop the corresponding geometrically nonlinear constrained Cosserat shell 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 strain measures. Notably, the role of the appearing new bending tensor is highlighted and investigated with respect to an invariance condition of Acharya [Int. J. Solids and Struct., 2000] which will be further strengthened.

References in corpus (3)

• Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations
• Derivation of a refined 6-parameter shell model: Descent from the three-dimensional Cosserat elasticity using a method of classical shell theory
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Cited by in corpus (5)

• A geometrically nonlinear Cosserat (micropolar) curvy shell model via Gamma convergence
• On in-plane drill rotations for Cosserat surfaces
• Linear constrained Cosserat-shell models including terms up to $O(h^5)$. Conditional and unconditional existence and uniqueness
• Shear stresses in fluid and solid membranes with bending elasticity
• Assorted remarks on bending measures and energies for plates and shells, and their invariance properties