Dramatic amplification of the flexoelectric effect in snapping surfaces

Abstract

Flexoelectricity exists in all inhomogeneously deformed dielectric materials and is greatly interesting in engineering science, especially in manufacturing microelectromechanical systems. However, the flexoelectricity is relatively small compared to the commonly known piezoelectricity. How to produce a considerably large flexoelectric effect and how to apply the effect to a large scale have concerned people for a long time. In this paper, we creatively enlarge the flexoelectric effect without decreasing the structure scale by harnessing the electromechanical instability—the snap-through instability—of a curved dielectric plate subjected to a concentrated load. We formulate the electrostatic energy of the system and obtain the governing equations by taking the first variation of the free energy. In the analysis, we find that the thickness of the plate and the initial configuration affect the onset of the snap-through. Beyond that, we notice that flexoelectricity can lower the critical load of the snap-through instability. Importantly, we find that a large flexoelectricity can be generated by harnessing the instability. For a dielectric plate with thickness 2 × 10−7 m, the effective electromechanical coefficient is equal to 35 pC/N in the beginning; however, by using the instability, the coefficient can be increased to as high as 740 pC/N, which is 21 times higher after the instability. In the end, we tune the electromechanical behaviors by designing the curved plate's thickness and configuration. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces.