Explicit formula for the Gamma-convergence homogenized quadratic curvature energy in isotropic Cosserat shell models

We show how to explicitly compute the homogenized curvature energy appearing in the isotropic $\mathrm{\Gamma }$-limit for flat and for curved initial configuration Cosserat shell models, when a parental three-dimensional minimization problem on $\mathrm{\Omega }\subset {\mathbb{R}}^3$ for a Cosserat energy based on the second order dislocation density tensor $\alpha :={\bar{R}}^T\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{l}\bar{R}\in {\mathbb{R}}^{3\times 3}$, $\bar{R}\in \mathrm{S}\mathrm{O}(3)$ is used.