Rate-dependent electro-mechanical deformation of nematic liquid crystal elastomers

Abstract

Theoretical modeling and numerical implementation of electro-viscoelastic interactions at finite strains of dielectric nematic Liquid Crystal Elastomers (LCE) are presented, capturing key phenomena such as Maxwell stress, director rotation, nonlinear deformations, the electric Fréedericksz transition, and energy dissipation. By combining continuum mechanics with Maxwell’s equations, governing equations for dielectric nematic LCEs are systematically derived via the principle of virtual power. The resulting thermodynamically consistent constitutive relations provide a relevant description of the coupled electro-mechanical and rate-dependent viscoelastic response, thereby enabling a reliable prediction of the material’s physical behavior. In addition to the electro-mechanical model, evolution equations for the viscous part of the deformation gradient are formulated using an internal variable approach, capturing the time-dependent dissipation characteristic of a generalized Maxwell’s rheological model. These equations are integrated using a fully implicit backward Euler scheme to ensure numerical stability and accuracy. Various deformation modes arising during the Fréedericksz transition are investigated, with particular attention to uniform expansion and thinning in the thickness direction as well as bending actuation observed in bi-layer samples. A fundamentally different actuation mode is demonstrated for bi-layer nematic LCE actuators, where reorganization of internal microstructures under an electric field enables two-sided actuation. Furthermore, electro-mechanical bulk instabilities such as buckling, arising from the combined effects of the Fréedericksz transition and Maxwell stresses, are analyzed. Special attention is given to rate-dependent behavior by demonstrating the effect of the electric potential ramp rate on deformation and on the emergence of buckling instabilities. Compared to classical dielectric elastomers, this behavior represents a more advanced mechanism with significant potential for next-generation active and soft robotic devices. Finally, the numerical simulations capturing the viscoelastic response are validated against experimental results from the literature to assess the accuracy and reliability of the proposed finite deformation model.