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.

基于变分原理，我们得出了介电液晶弹性体（LCE）中动量的平衡方程，Maxwell方程和非线性电光-机械耦合的指向矢场方程。此外，我们建立了一个简单的本构模型，以研究电场诱导的指向性取向随单畴向列型LCE的变形而发生的变化，这被称为固体Fréedericksz跃迁（SFT）。利用半解析法获得了无应力均质SFT的解。结果表明，如先前报道的实验所观察到的那样，LCE的半软弹性不足以模拟样品的超临界SFT。提出了对LCEs的半软弹性能的修改，以将SFT的亚临界特性改变为超临界。除了半分析方法外，还采用有限元方法来模拟将样品浸入介电液体中的实验。仿真结果与文献中的实验数据吻合良好。