A Geometrically Nonlinear Cosserat (Micropolar) Curvy Shell Model Via Gamma Convergence

Using $$\Gamma $$ -convergence arguments, we construct a nonlinear membrane-like Cosserat shell model on curvy reference configuration starting from geometrically nonlinear, physically linear three-dimensional isotropic model. Even if the theory is of order O(h) in thickness h, by comparison to membrane models proposed classical elasticity, beside change metric, still capable capturing transverse shear deformation and Cosserat-curvature due remaining effects. We formulate limit problem scaling both unknowns, microrotation tensor, expressing parental energy with respect fictitious flat configuration. The obtained via similar (no $$O(h^3)$$ flexural terms, but depending Cosserat-curvature) derived derivation approach, these two do not coincide. Comparisons other are also included.