Voltage-actuated snap-through in bistable piezoelectric thin films: a computational study

Bistable piezoelectric structures exhibit snap-through motions in response to applied voltage and play important roles in achieving functions such as fast actuation and structural morphing. However, modeling the nonlinear snap-through behaviors in such structures remains a challenge. In this paper, we develop a theoretical framework to model the voltage-actuated snap-through in bistable piezoelectric composites. Based on a revised continuum theory capable of characterizing the coupled finite deformation and electric field in piezoelectric materials, we establish a universal nonlinear finite element framework where the unknowns are the displacement and a scalar factor characterizing the magnitude of the applied voltage. By using the traditional Riks method, a supplementary arc-length equation related to the increment of the displacement and the scalar factor is constructed to complete the linearized incremental equation. A general solution scheme for obtaining the increments of all unknowns is developed, which enables automatic tracing of the nonmonotonic equilibrium path evolution. The feasibility and efficiency of this numerical method were demonstrated by the voltage-actuated snap-through phenomena for several bistable piezoelectric structures, including a simply-supported bilayer beam, a 3D square bilayer plate with free ends and a 3D constrained circular bilayer plate. This method will benefit the numerical design of high-performance bistable piezoelectric structures.