Deformative response of bilayer films to spatially non-uniform stimuli

Bilayer films are widely employed as actuators because of their ability to undergo bending deformations in response to environmental stimuli. While the bending curvature induced by uniform stimuli can be accurately described by the classical Stoney formula, predicting the deformation of bilayer films under spatially non-uniform stimuli remains challenging. The difficulty lies mainly in the coupling between the film’s responsive deformation and the local stimulus intensity that it experiences. To address this challenge, in this study, we extend the classical Stoney relation by developing a theoretical framework that links the local curvature of the film to the space-dependent stimulus intensity. This framework enables the precise prediction of the deformed configurations of bilayer films subjected to complex, non-uniform stimulus fields. The theoretical results are validated through finite-element simulations and experimental measurements, demonstrating excellent agreement. Our findings provide a solid theoretical foundation for controlling the responsive deformation of bilayer actuators to spatially varying stimuli, which facilitates the application and development of soft thin-film actuators.