Quasi-soft opto-mechanical behavior of photochromic liquid crystal elastomer: Linearized stress–strain relations and finite element simulations

Based on the neo-classical elastic energy of liquid crystal elastomers, the opto-mechanical behavior is modeled by considering the effect of photoisomerization on the nematic-isotropic transition of liquid crystal phase. Linearized stress–strain relation is derived for infinitesimal deformations with a very unusual shear stress that does not vanish identically as in the case of the soft behavior but is proportional to the rotation of directors. In other words, the shear stress depends on both the shear strain and the skew symmetric part of the displacement gradient with the shear modulus induced by the effect of photoisomerization. Finite element implementation for plane stress problems is obtained through a self-defined material subroutine in ABAQUS FEA tool. Numerical simulations show that the light induced deformations of two dimensional specimens consist of contractions, expansions and bending in different directions. The stress distributions indicate that the driving force for the light induced bending is produced by the bending moment of the normal stress along the director, while the other stress components are much smaller for two dimensional beam shaped specimens. However, the shear stress of the soft LCE is generally nonzero under light illumination due to the inhomogeneity of the opto-mechanical effect. It can be concluded from the strain distributions that the transversal plane cross section could remain plane after deformation if the light intensity or the decay distance is not too small and the sample is in the deep nematic phase. However, the shear strain and in plane rotation are of the same order as the other strain components, and thus should not be neglected. This indicates that the classical simple bending assumptions such as the Euler–Bernoulli beam theory should not be directly applied to model the light induced bending of neo-classical liquid crystal elastomers due to the soft behavior of the materials.