  In this paper, we study an elastic bilayer plate composed of a nematic liquid
crystal elastomer in the top layer and a nonlinearly elastic material in the
bottom layer. While the bottom layer is assumed to be stress-free in the flat
reference configuration, the top layer features an eigenstrain that depends on
the local liquid crystal orientation. As a consequence, the plate shows
non-flat deformations in equilibrium with a geometry that non-trivially depends
on the relative thickness and shape of the plate, material parameters, boundary
conditions for the deformation, and anchorings of the liquid crystal
orientation. We focus on thin plates in the bending regime and derive a
two-dimensional bending model that combines a nonlinear bending energy for the
deformation, with a surface Oseen-Frank energy for the director field that
describes the local orientation of the liquid crystal elastomer. Both energies
are nonlinearly coupled by means of a spontaneous curvature term that
effectively describes the nematic-elastic coupling. We rigorously derive this
model as a {\Gamma}-limit from three-dimensional, nonlinear elasticity. We also
devise a new numerical algorithm to compute stationary points of the
two-dimensional model. We conduct numerical experiments and present simulation
results that illustrate the practical properties of the proposed scheme as well
as the rich mechanical behavior of the system.
