Photoinduced Deformations of Beams, Plates, and Films

Photoresponsive solids such as nematic photoelastomers can undergo large deformations induced by light absorbed into rodlike molecules which bend and disrupt liquid crystal order. Significant variation of photoabsorption through the solid leads to nonuniform elastic deformations such as bending of beams and plates and pitting of layers. Such effects are also found in the presence of inhomogeneous thermal or swelling fields in solids or gels. We analyze the small deflection limit of these problems and show that beams made of these materials can have two elastically neutral planes, and that plates of these materials have a typical saddle shape. We also give a scaling analysis of the elasticity of photoinduced mounds and pits and speculate on their applications.

Figure 1

A photobeam, initially straight and illuminated from below, contracts more where the light is less attenuated. The curvature induced is $R$. A neutral surface is at $x_n$.

Figure 2

The dimensionless beam curvature $w/CR$ and the dimensionless location $x_n/w$ of the neutral surfaces as functions of scaled penetration depth $d/w$. The $x_n/w$ asymptotes $\frac{1}{2}(1\mp 1/\sqrt{3})$ (dotted line) are rapidly approached as $d/w$ increases.

Figure 3

The scaled elastic $zz$ strain $e(x)/C$ as a function of $x/w$ for different scaled penetration depths $d/w=0.05$, $0.5$, and $5$, the last exaggerated $\times 20$ for visibility.

Figure 4

A spot of light of radius $a$ induces the thickness $H$ of a photoelastomer, to increase by $u_{zz}H$. A trough of depth $\delta$ around the spot conserves volume. The healing length for distortions is $l\sim H$. Displacements $u_r$ and $u_z$ and resulting shears are sketched.