Nonlocal model of electromechanical fields and effective properties of piezoelectric materials with rigid and electrically conductive inclusions

A rigid and electrically conductive line inclusion (or electrode) in piezoelectric materials is considered under the framework of nonlocal effects for the stress and electric displacement fields. Both the piezoelectric medium and the inclusion are of finite size. The poling direction of the piezoelectric medium and the plane of inclusion are parallel. Electromechanical fields and the equivalent values of the elastic modulus, piezoelectric constants and dielectric constants along the inclusion direction are evaluated. The effect of the nonlocal parameter of the piezoelectric material is particularly remarkable for the stress and electric displacement fields. The maximum stress and electric displacement close the inclusion tip reduce as the nonlocal effect of the medium become stronger. However, the effective electromechanical properties of the piezoelectric medium do not have an apparent dependence on the nonlocal effect.