Abstract
The flexoelectric effect of materials, which is the coupling between strain gradient and electric polarization, is most noticeable for the micro/nano electromechanical systems. In the present paper, the size-dependent electromechanical properties of the bilayer piezoelectric sensor are studied and analyzed considering the strain gradient elastic and flexoelectric effects. The governing equation and the corresponding generalized mechanical boundary conditions of the bilayer cantilever sensor are derived utilizing the variational method of flexoelectric materials based on the electric Gibbs free energy. And a new piezo-flexoelectric coupling parameter is proposed and the relationship between the induced electric potential (voltage) and the rotation angles of the ends is obtained. The analytical expressions of deflection and induced electric potential are given when the bilayer piezoelectric sensor is subject to a uniform force. The numerical results show that the normalized deflection, normalized stiffness and induced electric potential are dependent on the structural size, material parameters and internal material length scale parameters. The piezoelectric effect will play a leading role in the induced electric potential when the sensor thickness is larger than a critical value. With decreasing sensor thickness, the flexoelectric and strain gradient elastic effects will dominate the induced electric potential. Moreover, an intrinsic size depending on the material properties is identified for the maximum induced electric potential. The thickness and polarization direction of the piezoelectric layer also have a great influence on the induced electric potential of the sensor systems.
Highlights
Piezoelectric/ferroelectric materials, which exhibit the excellent electromechanical coupling property, are widely used for actuators, sensors, energy harvesters and nonvolatile memories
We address the electromechanical responses of bilayer piezoelectric sensors due to flexoelectricity and strain gradient elasticity
The induced electric potential and deflection are given as analytical expressions for the static bending problem
Summary
Piezoelectric/ferroelectric materials, which exhibit the excellent electromechanical coupling property, are widely used for actuators, sensors, energy harvesters and nonvolatile memories. Introducing the flexoelectric effect into the linear piezoelectricity theory, Majdoub et al. firstly discussed the electromechanical coupling responses of the nano-beams with strain gradient Their results show that the piezoelectric and flexoelectric effects exhibit a nonlinear interaction. Using the internal energy theory, Yan and Jiang analyzed the mechanical and electrical properties of static bending flexoelectric nano-beams under the different mechanical boundary conditions, which shows that the elastic response is sensitive to the mechanical boundary conditions and the direction of applied electric filed He et al. established a geometrically nonlinear piezoelectric plate model with the piezoelectric and flexoelectric coupling. The influences of structural sizes, piezo- and flexoelectric parameters and material length scale parameters of strain gradient elasticity on the induced electric potential, normalized deflection and normalized stiffness are analyzed and discussed, emphasizing the fundamental distinguishing features of flexoelectricity as compared to piezoelectricity.
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