Study on the mechanical behavior of a bistable beam under third-order mode deformation

• An analytical model for third-order mode deformation of the bistable beam during the snap-through process has been established. • The criteria for judgment for the mutual switching between the two modes in the snap-through process of the bistable beam are provided. • It was found that for bistable beams of the same size, the work done by the external force during the third-order mode deformation process is twice that of the second-order mode deformation process. • This finding will provide a new design approach for the application of bistable beams in energy-dissipating materials. Bistable beams, with their characteristic recoverable elastic large deformations, are widely utilized in reversible deformation designs. However, analytical modeling of bistable beams under third-order mode deformation remains a challenge. For example, theoretical research on bistable beams in existing energy-consuming materials has focused mainly on the deformation process of the second-order mode. To address this challenge, the present work establishes an analytical model for the deformation process of a bistable beam from the first-order mode to the third-order mode via the elliptic integral method. Additionally, judgment conditions for identifying the critical points of modal transitions are provided. Second, the analytical model allows for the calculation of the maximum instability force and the unstable equilibrium position when third-order mode deformation occurs in the bistable beam during the snap-through process. The unstable equilibrium position of the bistable beam during third-order mode deformation is significantly lower than the positions of the two fixed ends. The validity of the analytical model was confirmed through experiments and finite element modeling. In the compression experiments of bistable beams with identical dimensional parameters presented in the present work, the work done by the external force during the third-order mode deformation process is 2 times that of the second-order mode deformation process. This will provide a completely new approach for the design of energy-consuming materials based on bistable beams.