Modeling and numerical simulation of thermo-electro-mechanical coupling behaviors of liquid crystal elastomers

Liquid crystal elastomer (LCE), as a newly emerging soft material, has been extensively explored to construct diverse structures for a wide range of applications. Many unique yet complex properties of LCEs originate from the tight coupling between the alignment of liquid crystal mesogens and the deformation of polymer network. It makes the modeling and simulation of the deformation of LCEs caused by the actions of multiple external stimuli very challenging. In this work, we formulate a theoretical framework to model the intricate behaviors of LCEs with thermo-electro-mechanical coupling and derive analytical solutions for homogeneous deformation. To implement the model in finite element simulation, a numerical approach that employs a quasi-convexified free energy function and achieves a key transformation of reference configuration is proposed. The numerical approach is further developed into a user subroutine for the commercial software ABAQUS. Various simulations are conducted by using it to validate the effectiveness of the model and numerical approach, as well as to demonstrate their potential applications. We hope the current work, particularly the developed program, provides a useful tool for various researchers to study the complex phenomena of LCEs.