LAUSR

We study the contribution of arbitrarily varied surface piezoelectricity to the anti-plane deformation and in-plane electric fields of a hexagonal piezoelectric material containing a finite crack. The varied surface piezoelectricity is incorporated by using an extended version of the continuum-based surface/interface model of Gurtin and Murdoch. In our discussion, the surface properties, including the surface elastic stiffness, the surface piezoelectric modulus and the surface dielectric permittivity, are assumed to be varied arbitrarily along the crack surfaces. By using the Green's function method, the original boundary value problem is reduced to a system of two coupled first-order Cauchy singular integro-differential equations. Through a diagonalization strategy, the coupled system is transformed into two independent singular integro-differential equations, each of which can be numerically solved by using the collocation method. Our results indicate that the variation of the surface electroelastic moduli exerts a significant influence on the crack opening displacement, the electric potential jump across the crack faces and on the strengths of the logarithmic singularity in stresses and electric displacements at the crack tips.