Stresses in a Thin Piezoelectric Element Bonded to a Half-Space

In this paper, a thin piezoceramic element is considered which is bonded to an elastic or a rigid half-space. Such a model may be an approximation of the interaction between piezoceramic elements and elastic structures like beams and plates. For an elastic half-space, the determination of the shear stress in the bonding layer leads to a singular integral equation. A half-space which is very stiff may be modeled as a rigid substrate. For this case, displacement functions are introduced. Hamilton’s principle for electromechanical systems allows the use of Lagrange multipliers to incorporate the condition of a stress free upper surface of the piezoceramic element. The stresses in the bonding layer and in the piezoceramic element are estimated by this method and compared with Finite Element results. Though the singularity near the ends of the piezoceramic element cannot be modeled by both methods, stress concentrations can clearly be seen for the shear stress as well as for the normal stress. As infinite stresses due to the singularity do not occur in reality, the results allow an estimation of the bonding stresses except in the near vicinity of the edges. The knowledge of these stresses is important to prevent failure due to delamination.