Continuum modeling of the nonlinear electro-opto-mechanical coupling and solid Fréedericksz transition in dielectric liquid crystal elastomers

Highlights

• Nonlinear electro-opto-mechanical coupling in dielectric nematic elastomers is simulated.

• Governing and constitutive equations are derived based on the variational approach.

• A modification of the semi-soft elastic energy of nematic elastomers is proposed.

• The subcritical character of the solid Fréedericksz transition is changed to supercritical.

• Analytical and finite element solutions for the solid Fréedericksz transition are obtained.

Abstract

Based on the variational principle, we derive the balance equation for momentum, Maxwell equation, and the equation of director fields for nonlinear electro-opto-mechanical coupling in dielectric liquid crystal elastomers (LCEs). Further, we establish a simple constitutive model to study the electric-field-induced director reorientation with the deformation of monodomain nematic LCEs, which is called the solid Fréedericksz transition (SFT). Semi-analytical method is utilized to obtain the solutions of stress-free homogeneous SFT. The results indicate that the semi-soft elasticity of LCEs is insufficient to simulate the supercritical SFT of samples, as observed in earlier reported experiments. A modification of the semi-soft elastic energy of LCEs is proposed to change the subcritical character of the SFT to supercritical. In addition to the semi-analytical methods, finite element method is employed to simulate the experiments in which samples are immersed in dielectric liquids. The simulation results show good agreement with the experimental data from literature.