  In this paper, the two-dimensional pure bending of a hyperelastic substrate
coated by a nematic liquid crystal elastomer (abbreviated as NLCE) is studied
within the framework of nonlinear elasticity. The governing system, arising
from the deformational momentum balance, the orientational momentum balance and
the mechanical constraint, is formulated, and the corresponding exact solution
is derived for a given constitutive model. It is found that there exist two
different bending solutions. In order to determine which the preferred one is,
we compare the total potential energy for both solutions and find that the two
energy curves may have an intersection point at a critical value of the bending
angle $\alpha_c$ for some material parameters. In particular, the director $\bm
n$ abruptly rotates $\dfrac{\pi}{2}$ from one solution to another at
$\alpha_c$, which indicates a director reorientation (or jump). Furthermore,
the effects of different material and geometric parameters on the bending
deformation and the transition angle $\alpha_c$ can be revealed using the
obtained bending solutions. Meanwhile, the exact solution can offer a benchmark
problem for validating the accuracy of approximated plate models for liquid
crystal elastomers.
