Nonlocal fields and effective properties of piezoelectric material with a rigid line inclusion perpendicular to the poling direction

A rigid line inclusion in a piezoelectric medium is studied under the framework of nonlocal piezoelectric elasticity. The two-dimensional problem in the (x, y) plane is considered and the piezoelectric medium and the inclusion are of finite size. The poling direction of the piezoelectric medium is perpendicular to the plane of inclusion and the problem is solved by singular integral equation technique. The electromechanical fields and the equivalent elastic modulus along the inclusion direction are obtained. It is found that the nonlocal effect can significantly reduce the stress concentration and the electric displacement level near the inclusion tip. Essentially, based on the nonlocal model, the stresses and electric displacements are finite at the inclusion tips. The maximum values of the stress and electric displacement reduce with increase in nonlocal parameter of the medium. The stiffness of the medium is also enhanced because of the rigid inclusion. The model is verified by the finite element method for the special case of local piezoelectric elasticity.