A constitutive model of liquid crystal elastomers with loading-history dependence

Liquid crystal elastomers (LCEs) are a class of active polymers of increasing interest, because of their excellent actuation performances. To quantify the actuation performances and understand the thermomechanical behavior, many theoretical models were developed, mainly based on the free energy framework with uniaxial order tensor, which, however, cannot well capture the biaxial liquid crystal alignment under biaxial stretching or shearing. The LCE with the shape memory cycle effect exhibits an evident loading-history dependence of the thermomechanical process, which cannot be described without introducing the evolution condition of the alignment. In this work, a constitutive model of LCE is established by introducing a triaxial order tensor to describe the complex alignment under uniaxial/biaxial loading conditions. Inspired by the classical theory of plasticity, an equivalent order parameter is proposed to characterize the order degree of the alignment, and its evolution condition is introduced to specify the condition of the alignment evolution. Experiments of LCE under a variety of thermomechanical loading conditions were carried out to validate the developed model, showing the capability of the model in capturing complex thermomechanical responses of the polydomain LCE with shape memory cycle effect under uniaxial/biaxial stretching. Furthermore, the constitutive model can be extended to predict nonlinear stress-strain curves and actuation performances of LCE lattices, which hold promising potential for applications in soft actuators and flexible robots.