Elastic theory of ideal liquid crystal elastomers

Abstract: A liquid crystal elastomer (LCE) exhibits a two-way coupling between its mesogen order and network elasticity: the mesogen order sets the undeformed network conformation, and the network deformation reorients the mesogens. This coupling gives rise to large, reversible stimuli-responsive actuation, as well as to soft elasticity, a finite deformation at nearly zero stress. This article reviews the elastic theory of ideal LCEs, bridging single-chain statistics and continuum constitutive models. The "ideal" elastic behavior rests on the assumption of anisotropic Gaussian chains that retain no memory of the crosslinking state, such that rotating the director costs no free energy. The corresponding neo-classical free energy of a monodomain LCE is non-quasi-convex, with a continuous family of stress-free ground states, leading to thermally induced spontaneous deformation and soft elasticity accommodated by coexisting stripe domains. The quasi-convex relaxation of the free energy classifies the behavior of polydomain LCEs into three phases, each with a distinct macroscopic mechanical response depending on the stretch state. The ideal elastic theory can be further extended to incorporate additional behaviors and physical processes, including thermo- and photomechanical coupling, Frank elasticity from director distortion, semi-soft or non-soft behavior arising from network nonideality, and temperature- and rate-dependent viscoelasticity.