Boundary effect on the spontaneous deformation of a liquid crystal elastomer plate with arbitrary director orientation

Except for director orientation, the deformation modes of constrained liquid crystal elastomer thin plate display specimen geometry size dependence due to the boundary effect. In this paper, the effect of plate geometry size on the spontaneous deformation of a simply supported liquid crystal elastomer plate is studied. The relation between the deformation modes with director orientation and plate geometry size are investigated. Results show that the deformation modes are decided by the director orientation for a certain liquid crystal elastomer, but the geometry size affects the mode transformation with respect to the director. These results are supposed to be used in the design and application of liquid crystal elastomer-based smart actuators or sensors.

Figure 1

(a) Sketch of a simply supported rectangular LCE plate illuminated by downward light (the width of the plate changes from 0.4 $a$ to $a$); (b) the director n has an angle ϕ with xOy plane, and its projection in xOy plane has an angle θ with $x$ axis; (c) the light-induced transformation between trans and cis.

Figure 2

The boundary conditions for simply supported LCE plate edges.

Figure 3

The spontaneous bending configurations of the simply supported LCE square plate.

Figure 4

The contour maps for spontaneous bending of LCE square plate with $\varphi ={55}^{\circ }$ and (a) $\theta =0^{\circ }$ (b) $\theta ={30}^{\circ }$ (c) $\theta ={45}^{\circ }$ (d) $\theta ={60}^{\circ }$ (e) $\theta ={90}^{\circ }$ (f) $\theta ={120}^{\circ }$.

Figure 5

The contour maps for spontaneous bending of LCE square plate with $\varphi ={39}^{\circ }$ and (a) $\theta =0^{\circ }$ (b) $\theta ={30}^{\circ }$ (c) $\theta ={45}^{\circ }$ (d) $\theta ={60}^{\circ }$ (e) $\theta ={90}^{\circ }$ (f) $\theta ={120}^{\circ }$.

Figure 6

The regions of director orientation θ and ϕ that lead to different spontaneous deformation modes of LCE square plate $\left(\zeta =1\right)$.

Figure 7

The effect of plate dimension ratio on the maximum deflection area of simply supported LCE plate with $\theta ={90}^{\circ }, \varphi ={47}^{\circ }$ (transforming from unimodal shape to bimodal shape).

Figure 8

The effect of the plate dimension ratio on the maximum deflection area of simply supported LCE plate with $\theta ={90}^{\circ }, \varphi ={44}^{\circ }$ (transforming from unimodal shape to bimodal shape, and further to multimodal shape).

Figure 9

The effect of the plate dimension ratio on the maximum deflection area of simply supported LCE plate with $\theta ={30}^{\circ }, \varphi ={40}^{\circ }$ (transforming from multimodal shape to unimodal shape).

Figure 10

The effect of the plate dimension ratio on the maximum deflection area of unimodal shape with $\theta =0^{\circ }, \varphi ={60}^{\circ }$.

Figure 11

The effect of the plate dimension ratio on the division for spontaneous bending configurations of the LCE plate.