Continuum mechanical modeling of liquid crystal elastomers as dissipative ordered solids

Abstract Liquid crystal elastomers (LCEs) are special cross-linked polymer materials combining the large elastic deformability of elastomers with the orientational orders of liquid crystals. Here we develop a general framework of LCEs in the language of continuum mechanics to consider the interaction of polymer backbone and Liquid Crystal (LC) microstructure, which is suitable for large deformation and large director rotation. Based on the dissipation principle, the balance of momentum and the evolution equations of orientational order are obtained. In addition to the deformation and its time derivative, the basic kinematic ingredients of this theory are identical to those arising in the director theories and the order tensor theories for nematic fluids. The Cauchy stress consists of not only the bulk stress contribution of the backbone but also the Ericksen–Leslie stress of LC and the obtained rotational momentum balance implies the asymmetric Cauchy stress due to the inhomogeneous director rotation. Based on the principles of objectivity and symmetry, we present the general form of free energy densities and Rayleigh dissipation function and give some possible invariants of constitutive functions. Further, we propose a simple model to study the rate dependence of stretch induced reorientation processes for thin LCE films. Semi-analytical method is utilized to obtain the solutions of constrained uniaxial stretches and stretches with shear for homogenous deformations. The results indicate that the stress-deformation response and the director rotation are rate dependent and can be non-monotonic depending on the initial orientations. Finite element simulations are carried out to study the process of uniaxial stretches with fixed grips. Two different types of stress induced director reorientation processes are observed, one via stripe domains and the other via uniform rotations. We find that the appearance of the stripe domains has a strong dependence on aspect ratios and initial director orientation, which show good agreement with experiment results.