Modeling the coupling between viscoelasticity and soft elasticity in nematic liquid crystal elastomers

Liquid crystal elastomers (LCEs) are a unique class of smart materials with attractive mechanical properties, including high energy dissipation and soft elasticity. These behaviors arise from the structure of LCEs, where liquid crystal molecules (mesogens) are embedded within a polymer chain network. Under deformation, mesogens reorient along the applied load, producing soft elasticity—a notable increase in strain at a constant stress level. The rotation of mesogens, coupled with the viscoelastic nature of the polymer, results in a complex, nonlinear viscoelastic response. While these properties make LCEs appealing for many applications, several challenges limit their practical use, particularly the need to understand and model their nonlinear, coupled responses under various loading conditions.In this study, we first evaluated the presence of soft elasticity in polydomain LCEs under compressive loading and then investigated the coupling between soft elasticity and viscoelastic mechanisms in nematic LCEs under tensile and compressive conditions. We examined the compressive behavior of LCEs, focusing on the influence of mesogen orientation on viscoelastic mechanisms and assessing the presence of soft elasticity in compression. To model these complex behaviors, we initially proposed a rheological model in which meso- gen rotation is represented by a reversible slider, and viscoelastic relaxation mechanisms are modeled with a series of Maxwell elements that are either coupled or decoupled from mesogen rotation. Fitting this model to experimental tensile data revealed partial coupling between polymer chain viscoelasticity and mesogen rotation; specifically, long-term relaxation mechanisms are coupled to mesogen alignment, while short-term mechanisms remain decoupled. This finding deepens our understanding of the time-dependent mechanical response of LCEs during the polydomain-monodomain (PM) transition. We extended this model to a finite strain framework to accurately predict LCE stress responses under large deformations. By fitting the finite strain model to experimental data from both tensile and compressive tests, we examined differences in relaxation mechanisms and the effects of mesogen rotation across loading conditions. Finally, the finite strain model was implemented in the finite element software FEAP and FEBio, where its performance was evaluated through a plate with a hole simulation to capture complex stress distributions, demonstrating its ability to predict LCE behavior at various strain rates.