Effective shear modulus of piezoelectric film embedded with square nano-fibers under anti-plane shear waves

Abstract

For piezoelectric films, the surface/interface energy around the nano-fibers plays an important role in predicting the overall properties. Square nano-fibers are very popular in piezoelectric films. This paper presents the size-dependent dynamic effective elastic modulus of piezoelectric films under anti-plane shear waves. The average electro-elastic field resulting from the randomly distributed nano-fibers is solved by applying the effective field method. To express the coupling fields in the effective field, the mapping method and wave function expansion method are introduced. The closed-form solution of piezoelectrically stiffened shear modulus with respect to the shape and volume fraction of fibers and surface/interface properties is obtained. The interacting effect of surface/interface and square shape of nano-fibers is examined.