Light-induced wrinkling instability of confined annulus liquid crystal elastomer film

Authors of previous studies have focused on wrinkling phenomena in thin films with relatively large stiffness under mechanical loadings. A liquid crystal elastomer (LCE) is a smart soft material sensitive to various environmental stimuli. In this letter, we investigate the wrinkling instability of a confined LCE film with different inner hole sizes induced by light illumination. The LCE film is clamped at the outer edge and has a free inner edge. Based on linear perturbation analysis, we obtain the critical condition for the onset of wrinkling instability. Whether the film will remain flat or bifurcate into a wrinkled state is determined by the value of expansion coefficient, light intensity, inner hole size, and thickness of the LCE film. We find that a film with a bigger inner hole size corresponds to a large wrinkle number and show that the expansion coefficient of a LCE and light intensity can be used to adjust the wrinkling instability behavior and time consumption for the appearance of wrinkles.

Figure 1

Schematics of a confined liquid crystal elastomer (LCE) film (a) with outer radius $B$ containing an inner hole of radius $A$ in reference state. (b) The liquid crystal molecules aligned with the thickness direction will undergo trans-to-cis transition, leading to shrinkage in the thickness direction but expansion in the other film direction. Consequently, the LCE film may (c) remain a flat surface or (d) generate wrinkles around the inner hole in the deformed state.

Figure 2

The dimensionless radial and hoop stress distribution for (a) and (b) small hole sizes, along with (c) and (d) big hole sizes under different light illumination times. Negative stresses will be generated in both radial and hoop directions and there exists asymptotic stress distribution as the light illumination time goes infinitely.

Figure 3

(a) A phase diagram indicating the flat and wrinkled states under light illumination determined by expansion coefficient $C_0$ and $A/B$, (b) though in the same wrinkled states, the critical wrinkle number $k$ behaves differently for various $A/B$. The corresponding representative surface morphologies of wrinkling are shown in (c).

Figure 4

Phase diagrams of wrinkle and flat states influenced by different expansion coefficient $C_0$ and film thickness $H/B$ for (a) medium hole size and (b) big hole size. The film with a small thickness tends to deform into a wrinkled state when other conditions remain unchanged, but the wrinkle number is different.

Figure 5

The critical time ${\overline{t}}_w$ for the appearance of wrinkles as a function of (a) dimensionless light intensity $\overline{I}$ and (b) expansion coefficient $C_0$.