Living creatures routinely extract energy from the environment and use it to power mechanical deformations of soft tissues. Creating synthetic systems with these capabilities is an outstanding challenge and is the goal of the emerging field of soft robotics.
In this work, we show the first example of an autonomous shape-morphing sheet and provide a model for this system. We build a thin gel whose swelling state is coupled to the Belousov-Zhabotinsky (BZ) reaction. The reaction extracts free energy from the environment, and its temporal-spatial patterning drives the periodic flapping-like motion. Using the theory of non-Euclidean elasticity, we establish a constitutive relation between the Gaussian curvature of the sheet and the phase of the reaction.
I. Levin, R. Deegan, and E. Sharon, Self-Oscillating membranes: chemo-mechanical sheets show autonomous periodic shape-transformation. Phys. Rev. Lett. 2020 125(17)