A large deflection light-induced bending model for liquid crystal elastomers under uniform or non-uniform illumination

In this paper, we propose a large deflection model for the light-induced bending of liquid crystal elastomers, in which we consider the in-plane membrane force and the geometrical nonlinearity. Based on the Hamilton principle, we derive the in-plane force balance equation and the dynamic deflection curve differential equation. The effect of light on the bending is defined as an effective optical bending moment, which is generated by the inhomogeneous light-induced strain and the membrane force. By coupling solving these two equations, we can obtain the deflection curves of LCEs under any boundary conditions and illumination. As examples, we solve the equations by an analytical-numerical method and simulate the bending under uniform illuminations. Then we consider the situations of non-uniform laser illumination and solve the equations by finite difference method. The deflection of the LCE sample can be varied and controlled by changing the illumination position, the illumination direction, the light intensity and the distribution half width of the electric field. As a result, when the LCE sample is constrained at the two boundaries, the small deflection bending theory is no longer applicable, and we need to use the large deflection theory.