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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.
Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these i
The director configuration of disclination lines in nematic liquid crystals in the presence of an external magnetic field is evaluated. Our method is a combination of a polynomial expansion for the director and of further analytical approximations wh
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We consider a mathematical model that describes the flow of a Nematic Liquid Crystal (NLC) film placed on a flat substrate, across which a spatially-varying electric potential is applied. Due to their polar nature, NLC molecules interact with the (no