  In this paper we extend the recently introduced mixed Hellan-Herrmann-Johnson
(HHJ) method for nonlinear Koiter shells to nonlinear Naghdi shells by means of
a hierarchical approach. The additional shearing degrees of freedom are
discretized by H(curl)-conforming N\'ed\'elec finite elements entailing a shear
locking free method. By linearizing the models we obtain in the small strain
regime linear Kirchhoff-Love and Reissner-Mindlin shell formulations, which
reduce for plates to the originally proposed HHJ and TDNNS method for
Kirchhoff-Love and Reissner-Mindlin plates, respectively. By using the Regge
interpolation operator we obtain locking-free arbitrary order shell methods.
Additionally, the methods can be directly applied to structures with kinks and
branched shells. Several numerical examples and experiments are performed
validating the excellence performance of the proposed shell elements.
