A constitutive model of monodomain liquid crystal elastomers with the thermal-mechanical-nematic order coupling

Liquid crystal elastomers (LCEs) are a distinctive class of materials that combine the transformative properties of liquid crystals with the flexibility of elastomers, enabling significant reversible deformations in response to various external stimuli. This paper investigates the intricate thermal-mechanical-nematic order coupling behaviors of monodomain nematic LCEs. We propose an enhanced constitutive model that merges the established neo-classical theory with the Landau–de Gennes theory, thereby improving the model's ability to account for temperature influences effectively. Additionally, we use the concept of semi-soft elastic energy and consider the anisotropic behaviors associated with the orientations of the nematic directors, aiming to more accurately capture the nuances of their soft elastic and anisotropic properties under varied loading conditions. The present model has been numerically discretized and implemented in the commercial finite element software, facilitating precise simulations of the stress-stretch relationships and the anisotropic mechanical behaviors associated with specific director orientations. Constitutive simulations have shown a high degree of accuracy, aligning well with experimental data, especially in predicting the complex mechanical behaviors of LCEs under different thermal-mechanical conditions. Our results elucidate the necking observed during uniaxial loading and the unique director evolution during biaxial loading. Additionally, we identify a unique hole-size insensitivity in perforated LCE sheets, attributed to the compensation between anisotropic reinforcement and director orientations. These findings underscore the potential of advanced modeling techniques in exploring the dynamic properties of LCEs, paving the way for applications in artificial muscles, soft robotics, and responsive biomedical devices.