Arbitrary curvature programming of thermo-active liquid crystal elastomer via topology optimization

Plants can change their morphology upon environmental variations such as temperature. Inspired by plants’ morphological adaptability, we present a computational inverse design framework for systematically creating optimized thermo-active liquid crystal elastomers (LCEs) that spontaneously morph into arbitrary programmed geometries upon temperature changes. The proposed framework is based on multiphysics topology optimization and a statistical mechanics-based LCE model to realize arbitrary curvature programming for LCE composites under large deformations. We propose a curvature-based optimization formulation that enables rotation-invariant and size-insensitive programmability of LCE, accounting for its highly nonlinear deformed shape. We demonstrate that the programmed LCE composites can accurately morph into a wide range of complex target shapes and curvatures, such as those of numbers, letters, flowers, and various objects. The resulting optimized designs exhibit highly irregular material distributions, which surpass intuition-based designs, and precisely produce desired deformed geometries upon temperature increase. The computational inverse design technique holds promise for a wide array of applications requiring function- and performance-driven design of active materials.