  In the context of finite elasticity, we propose plate models describing the
spontaneous bending of nematic elastomer thin films due to variations along the
thickness of the nematic order parameters. Reduced energy functionals are
deduced from a three-dimensional description of the system using rigorous
dimension-reduction techniques, based on the theory of Gamma-convergence. The
two-dimensional models are nonlinear plate theories in which deviations from a
characteristic target curvature tensor cost elastic energy. Moreover, the
stored energy functional cannot be minimised to zero, thus revealing the
presence of residual stresses, as observed in numerical simulations. The
following three nematic textures are considered: splay-bend and twisted
orientation of the nematic director, and uniform director perpendicular to the
mid-plane of the film, with variable degree of nematic order along the
thickness. These three textures realise three very different structural models:
one with only one stable spontaneously bent configuration, a bistable one with
two oppositely curved configurations of minimal energy, and a shell with zero
stiffness to twisting.
