Topology optimization of programmable and fabricable thermo-active liquid crystal elastomer with continuous director orientations

Liquid crystal elastomer (LCE) is a soft active material capable of large, reversible actuation upon temperature changes, making it an ideal candidate for applications in smart structures, soft robotics, and sensors. Topology optimization of LCE can enable strategically distributed director patterns to fully exploit its multiphysics mechanism. However, existing approaches often miss to account for manufacturability. Aiming to produce fabricable optimized LCE structures and to further expand design space, this study proposes a general topology optimization framework for LCE under large deformations to simultaneously optimize free-form geometry and continuous LCE director distributions that are suitable for Direct Ink Writing (DIW). The framework is built upon a rigorous model to accurately capture LCE’s large thermal deformation, with a novel continuation filtering technique to realign LCE directors smoothly, accounting for LCE’s unique physical properties. With the proposed method, we present several optimization formulations to design various complex and intriguing LCE behaviors under temperature changes, including programmable complex shape morphing, inducing desired strains for biological tissues, and achieving non-monotonic thermal expansion–contraction under a monotonic temperature rise. The optimized LCE designs successfully achieve versatile desired functionalities while featuring a continuous director distribution suitable for DIW fabrication. Our findings will facilitate the discovery of arbitrarily manipulatable and physically realizable LCE responses, expanding the horizon for multi-physics active materials.