Curvature Induced by Deflection in Thick Meta‐Plates

The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non‐Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta‐plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome‐like and saddle‐like shapes. Depending on the unit cell structure, non‐auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta‐plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta‐plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D‐printed microscale meta‐plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented. The design of advanced functional devices often requires intrinsically curved geometries that belong to the realm of non‐Euclidean geometry. Thick meta‐plates based on hexagonal cellular mesostructures are used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures. A scaling relationship is presented to predict the deformation‐induced curvature of thick plates and their micro‐architectural design variables.