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Using a geometrically motivated 8-parameter ansatz through the thickness, wereduce a three-dimensional shell-like geometrically nonlinear Cosserat materialto a fully two-dimensional shell model. Curvature effects are fully taken intoaccount. For elastic isotropic Cosserat materials, the integration through thethickness can be performed analytically and a generalized plane stresscondition allows for a closed-form expression of the thickness stretch and thenonsymmetric shift of the midsurface in bending. We obtain an explicit form ofthe elastic strain energy density for Cosserat shells, including terms up toorder $O(h^5)$ in the shell thickness $h$. This energy density is expressed asa quadratic function of the nonlinear elastic shell strain tensor and thebending-curvature tensor, with coefficients depending on the initial curvatureof the shell.

Refined dimensional reduction for isotropic elastic Cosserat shells with initial curvature