Bending-induced director reorientation of a nematic liquid crystal elastomer bonded to a hyperelastic substrate

Bending deformation of nematic liquid crystal elastomers (abbreviated as NLCEs) serves not only as a benchmark but also as a basic action of soft robots. It is, therefore, of fundamental importance to carry out a thorough analysis of finite bending of NLCEs. This paper studies such a problem by coating an NLCE to a hyperelastic substrate. The aim is to derive the analytical solution and investigate whether or not different constitutive models of NLCEs can drastically affect the theoretical predictions. For that purpose, four NLCE models are considered. The governing system of each case is established, and solving it leads to two different bending solutions. In order to determine which is the preferred one, we compare the total potential energy for both solutions and find that the two energy curves may have an intersection point at α_c, a critical value of the bending angle, for some material parameters. In particular, the director n abruptly rotates π/2 from one solution to another at α_c, which indicates a director reorientation. By applying the solution procedure to different material models, we find that the theoretically predicted behavior is dependent on the material models applied. Besides unraveling a possible director reorientation in a bent NLCE, the current work also suggests that an experimental investigation on bending may be a good way for selecting a suitable constitutive relation for practical applications.