  We review different (reduced) models for thin structures using bending as
principal mechanism to undergo large deformations. Each model consists in the
minimization of a fourth order energy, potentially subject to a nonconvex
constraint. Equilibrium deformations are approximated using local discontinuous
Galerkin (LDG) finite elements. The design of the discrete energies relies on a
discrete Hessian operator defined on discontinuous functions with better
approximation properties than the piecewise Hessian. Discrete gradient flows
are put in place to drive the minimization process. They are chosen for their
robustness and ability to preserve the nonconvex constraint. Several numerical
experiments are presented to showcase the large variety of shapes that can be
achieved with these models.
