A gradient model of light-induced bending in photochromic liquid crystal elastomer and its nonlinear behaviors

Photochromic liquid crystal elastomer was recently reported to be able to deform largely and bend under illumination. In this paper, considering the opto-chemical process and the nematic–isotropic phase transition, we introduce the light and temperature into the constitutive relation of the liquid crystal elastomers, and propose a model for the light-induced bending. The dynamic deflection curve equation of the light-induced bending is derived based on the Hamilton principle. In the equation, the effect of light is introduced as an effective optical bending moment, which is caused by the inhomogeneous light-induced strain and Young's modulus. Several simulation examples are given to show the light-induced bending under different boundary conditions and various illumination or temperature controlling. Under the condition of deep nematic phase and weak enough illumination, the approximate analytical expression of the effective moment and the stress distribution can be obtained. Rich nonlinear behaviors are found in this model. The effective moment is a non-monotonic function of time, thickness ratio, and light intensity when the thickness ratio is not very large. The stress distribution through the thickness is nonlinear with two or three zero-stress planes.