Light-responsive liquid crystal elastomers (LCEs) have been at the forefront of stimuli-responsive actuators in the recent past. The light-responsive elastomers are created by doping the elastomeric network with the azo-benzene mesogens. The elastomeric network's weak cross-linking and the mesogen's order-disorder transition lead to certain exotic behaviours, as mentioned below.
1. The stretching of poly-domain LCEs results in the uni-axial alignment of the mesogens.
2. The rise in temperature leads to Nematic-Isotropic transitions and large deformations.
3. The weak cross-linking of the elastomers coupled with trans-cis isomerisation of the azo-benzene leads to changes in the alignment of the elastomer resulting in large mechanical deformations upon illumination (Photo-mechanical coupling).
In this study, we have developed a user element subroutine (UEL) using the commercial finite element software Abaqus to simulate the photomechanical coupling of these nematic elastomers subjected to mechanical stress and illumination. To model the photomechanical coupling using the finite element method, the minimisation of the free energy approach is implemented considering Corbett and Warner's formulation for polymeric network elastic behaviour and Maier-Saupe theory-based formulation for nematic liquid crystal behaviour. A system of linear equations with displacements, order-parameter and the alignment direction as primary variables is developed following the Rayleigh-Ritz and Newton-Raphson's method. The developed model is benchmarked by comparing the result of a 2D LCE sheet with the literature. Moreover, the developed UEL is then used to simulate the exotic behaviours of the LCE sheets discussed earlier. The developed framework can also be extended to simulate the coupled photomechanical response of LCEs with patterned/varying alignment distributions.