On equations of Cosserat-type shells

A review of the family of the Cosserat-type nonlinear shell theories is presented. Starting with a general directed deformable surface model with p directors, we consider different elastic shell models using the direct approach. For derivation of the governing equations, we use the principle of virtual work and the principle of material frame-indifference applied to the surface density of a strain function. We discuss the interrelation between the most popular models, such as the directed surface model with one deformable director, the micromorphic and micropolar shell models, and the Timoshenko-Reissner-Mindlin model.