Rate-dependent stress-order coupling in main-chain liquid crystal elastomers

Liquid crystal elastomers (LCEs) exhibit significant viscoelasticity. Although the rate-dependent stress-strain relation of LCEs has already been widely observed, the effect of the intricate interplay of director rotation and network extension on the viscoelastic behavior of main-chain LCEs remains inadequately understood. In this study, we report real-time measurements of the stress, director rotation, and all strain components in main-chain nematic LCEs subjected to uniaxial tension both parallel and tilted to the initial directors at different loading rates and relaxation tests. We find that both network extension and director rotation play roles in viscoelasticity, and the characteristic relaxation time of the network extension is much larger than that of the director rotation. Interestingly, the gradual change of the director in a long-time relaxation indicates the director reorientation delay is not solely due to the viscous rotation of liquid crystals but also arises from its coupling with the highly viscous network. Additionally, significant rate-dependent shear strain occurs in LCEs under uniaxial tension, showing non-monotonic changes when the angle between the stretching and the initial director is large enough. Finally, a viscoelastic constitutive model, only considering the viscosity of the network by introducing multiplicative decomposition of the deformation gradient, is utilized to manifest the relation between rate-dependent macroscopic deformation and microscopic director rotation in LCEs.