Derivation of a refined 6-parameter shell model: Descent from the three-dimensional Cosserat elasticity using a method of classical shell theory

Starting from the three-dimensional Cosserat elasticity, we derive a two-dimensional model for isotropic elastic shells. For the dimensional reduction, we employ a derivation method similar to that used in classical shell theory, as presented systematically by Steigmann in [J. Elast. \textbf{111}: 91-107, 2013]. As a result, we obtain a geometrically nonlinear Cosserat shell model with a specific form of the strain-energy density, which has a simple expression with coefficients depending on the initial curvature tensor and on three-dimensional material constants. The explicit forms of the stress-strain relations and the local equilibrium equations are also recorded. Finally, we compare our results with other 6-parameter shell models and discuss the relation to the classical Koiter shell model.

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