Energy Minimizing Configurations for Single-Director Cosserat Shells

We consider a class of single-director Cosserat shell models accounting for both curvature and finite mid-plane strains. assume polyconvexity condition the stored-energy function that reduces to physically correct membrane model in absence bending. With appropriate growth conditions, we establish existence energy minimizers. The local orientation minimizing configuration is maintained via blowup stored as version volume ratio approaches zero. Finally, specialize our results three constrained versions theory commonly employed subject.