Shape Morphing and Instabilities in Twisted Nematic Elastomer Shells

Liquid Crystal Elastomers are soft and stimuli-responsive materials, highly directional analogous to muscle fibers. Inspired by morphogenetic events and muscle morphologies - where critical shape transformations are driven by instabilities - we study the geometry of Twisted Nematic Liquid Crystal Elastomers (TNLCEs). While existing studies have primarily focused on simpler topologies such as twisted nematic discs, we present a first principles derivation of a dimensionally reduced model, using non-Euclidean plate theory for cylindrical shells with complex twist configurations. Our effective elasticity model captures an anomalous energy penalty associated with curvature induced by the twist. This emergent term arises from the interplay between orientational order and elasticity, dominating traditional bending contributions and rendering the system susceptible to instabilities. We explore the stability criteria associated to our model and make predictions about the resulting equilibrium shapes driven by the effective elasticity. Our simplified model allows for the study of shape morphing in TNLCEs and enables the design of tunable surfaces by leveraging instabilities, with potential applications in soft robotics.