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. We assume a polyconvexity condition for the stored-energy function that reduces to a physically correct membrane model in the absence of bending. With appropriate growth conditions, we establish the existence of energy minimizers. The local orientation of a minimizing configuration is maintained via the blowup of the stored energy as a version of the local volume ratio approaches zero. Finally, we specialize our results to three constrained versions of the theory commonly employed in the subject.

Automated summary

This paper studies a class of single-director Cosserat shell models that account for both curvature and finite mid-plane strains. By assuming a polyconvexity condition for the stored-energy function, a physically correct membrane model is obtained in the absence of bending. With appropriate growth conditions, the existence of energy minimizers is established. The local orientation of a minimizing configuration is maintained through the blowup of the stored energy as a version of the local volume ratio approaches zero.