Coupling Surface/Interface Theory And Effective Properties Of Nano-Sized Piezoelectric Materials

Due to the unique coupling between piezoelectric and semiconducting properties, nano-sized piezoelectric materials have a wide prospect applied in transducers, actuators and energy harvesters in the nano-electro-mechanical systems. Compared with the macroscopic piezoelectric composites, nano-sized piezoelectric materials exhibit physical properties due to their large ratio of surface area to volume. Surfaces/interfaces in nanostructures play a significant role in deciding the electro-mechanical coupling properties of piezoelectric nano-sized piezoelectric materials. Based on the Effective Field Method, the effect of the surface/interface on the effective properties in nano-sized piezoelectric materials is investigated systematically in this dissertation. The main research contents are as follows:Multiple scattering of anti-plane shear waves and dynamic effective electro-elastic properties in nano-sized piezoelectric materials with coated piezoelectric nano-fibers are investigated. By using the Effective Field Method of electric-elastic coupling wave, the randomly distributed coated nano-fibers in the piezoelectric media are reduced into a typical piezoelectric coated nano-fiber. Wave function expansion method is used to express the coupling wave field in the effective coupling field, and the expanded mode coefficients are determined by satisfied the boundary conditions at the surface/interface. The analytical solution of dynamic effective electro-elastic properties is obtained. Through analysis, it is found that the coupling surface/interface effect on the dynamic effective electro-elastic properties show significant variation with the material properties of coating layer.Based on Effective Field Method, the dynamic effective elastic modulus of polymer matrix composites embedded with dense piezoelectric nano-fibers is obtained. The interacting between the two typical piezoelectric nano-fibers is analyzed by employing the addition theorem of Bessel functions. Through numerical calculations, the influence of the distance between the two piezoelectric nano-fibers under different surface/interface parameters is analyzed. The effect of piezoelectric property of surface/interface on the effective shear modulus under different volume fractions is also examined.A comprehensive electro-mechanical model of nano-size is developed to predict the effective coupling properties of piezoelectric nano-sized piezoelectric materials with coated elliptical nano-fibers. Combining the generalized self-consistent method and the mapping method, a closed-form solution of the effective electro-mechanical coupling properties is derived. The effects of surfaces/interfaces around the coating layer and the shape of the nano-fibers on the effective properties are considered. Through numerical calculations, it is found that the elastic modulus and dielectric constant increase with the semi-major axes, while piezoelectric constant expresses different behavior.Based on the electro-elastic surface/interface theory, the effective elastic properties of piezoelectric ceramic embedded with radially polarized nano-fibers are addressed. The analytical solutions of elastic displacement and electric potentials are exactly derived by separating variables. The effective elastic responses of nano-sized piezoelectric materials are derived by satisfying the boundary conditions at surface/interface. Analyses show that the effective elastic properties can be enhanced by adjusting the material properties of the surface/interface.