Bistability of a Plate Driven by Geometric Asymmetry

Bistable structures that have two stable shapes are commonly seen in natural and synthetic systems such as the Venus flytrap and slap bracelets. These structures can switch from one stable shape to the other and stay as the new, stable configuration without continuing energy input, which can increase the energetic efficiency of the system. In addition, during the shape transition (snap-through), the stored potential energy will be suddenly released to accelerate the motion, decreasing the transition time that typically is not achieved by actuating mechanism based on the diffusion process. These unique properties make bistable structures promising candidates in actuators, deployable structures, energy harvesters, switches, valves, and micro-electro-mechanical systems (MEMS). Among various types of bistable structures, a thin sheet can take two different cylindrical shapes with opposite bending directions due to the interplay between the geometry and mechanics. To fabricate this type of bistable plates, previous works have utilized the asymmetric, mechanical pre-stressing or anisotropic deformation of stimuli-responsive materials to prescribe the required internal stress distribution. However, some of the reported methods require sophisticated synthesis of the constituent materials that can increase the fabrication time and costs. Therefore, it will be advantageous to develop a facile method to design and fabricate bistable structures by using geometric asymmetry.

In this paper, we provide a new scheme by mainly exploiting the plate’s asymmetric geometry. In experiments, we attach passive strips to both sides of a stretched, thin sheet, and bistability occurs when the strips’ pattern is asymmetric. Analysis based on the Föppl–von Kármán plate theory as well as finite element simulations are performed to quantitatively identify the relationship between the bistable behaviors and the geometric parameters of this triple-layered structure. As a result, the bifurcation and stability diagrams are plotted accordingly, and good agreement is found between the theoretical and computational predictions, which can provide quantitative understanding and guidance for the future design of this type of bistable plate. Moreover, we demonstrate that our triple-layered structure can realize various configurations such as helices and “gripper” by properly tuning the strips’ pattern through experiments and simulations. Since the equally biaxial pre-stretch of the middle layer in our design acts similarly to the isotropic response of smart materials, our prototype is compatible with many types of stimuli-responsive materials such as hydrogels as well as established techniques including photolithography and 3D printing. Thereby, properly combined with the functional materials, the results can enrich the existing design space of bistable and reconfigurable structures that can find a variety of applications such as in energy harvesting devices and soft robotics.