  We present a discontinuous Petrov-Galerkin (DPG) method with optimal test
functions for the Reissner-Mindlin plate bending model. Our method is based on
a variational formulation that utilizes a Helmholtz decomposition of the shear
force. It produces approximations of the primitive variables and the bending
moments. For any canonical selection of boundary conditions the method
converges quasi-optimally. In the case of hard-clamped convex plates, we prove
that the lowest-order scheme is locking free. Several numerical experiments
confirm our results.
