Coupling of a magnetic field with instability for multimodal and multistep deformations of a curved beam with asymmetric magnetic torque

Abstract A bistable curved beam with magnetic-torque-driven actuation has the potential for fast and untethered reconfiguration of metamaterials. However, there is currently no modeling method of a bistable curved beam for which the instability is coupled with an external magnetic field for the design of active metamaterials. The second mode (S-shape) generation of a bistable curved beam is essential for a multimodal and multistep reconfiguration of metamaterials and has not yet been explored. Herein, we aim to construct an analytical model of the deformation of a bistable curved beam triggered by an external magnetic field, providing magnetic-torque-driven multimodal and multistep deformations. We also implement symmetric and asymmetric magnet arrangements to the model to enable variation of the external magnetic fields to identify the range of the magnetic field's direction on the bistable and doubly curved transformations. Our instability model coupled with a magnetic field predicts multimodal and multistep deformations of bistable curved beams with magnetic torques triggered by the orientation and magnitude of the magnetic field. Our model reveals that i) a bistable curved beam without prestressing and ii) the asymmetric magnet arrangement design are favorable for generating an extensive range of the S-shape, which is significant for the design of multimodal transformation of metamaterials.