First order shear strain beam theory for spontaneous bending of liquid crystal polymer strips

Spontaneous bending induced by light and/or heat for beam shaped thin strips of crosslinked photochromic liquid crystalline polymer (LCP) materials is studied in this paper. Due to the possible presence of large transversal shear component of the spontaneous strain, we proposed a bending model by relaxing the classical normal cross-section assumption of Euler-Bernoulli beam theory. Our first order shear strain beam model considers the effect of the transversal spontaneous shear but not the elastic shear. So it does not require any shear correction factor as Timoshenko beam theory. Our model is valid for moderately thick to slender beams as comparing to finite element calculations. Analytical solutions show rather strong effect of spontaneous shear on bending of LCP strips with neither planar nor homeotropic alignment. Based on minimization of radiant power of light, we found that, by utilizing the spontaneous shear effect, a liquid crystalline orientation with a tilted angle to the beam axis can be energetically more favorable than the most studied planar alignment. An energy saving of 20% can be achieved by choosing the optimal orientation for thin beams (length/thickness ∼10) and even more for shorter ones. Our result is expected to be helpful to create desired and optimized bending for light or heat triggered sensing and actuation.