Abstract:
This study integrates Steigmann-Ogden surface elasticity theory with classical piezoelectric theory to establish a fully coupled electromechanical contact mechanics model for piezoelectric materials. This model comprehensively accounts for the surface mechanical effects, including surface residual stress, surface membrane stiffness and surface bending stiffness. By means of Fourier integral transforms and Gauss-Chebyshev numerical quadrature method, the distributions of contact pressure, contact stress, and electric displacement in a piezoelectric half-plane under a rigid circular indenter are obtained. The dependencies of these electromechanical responses on the surface elastic moduli and size of indenter are analyzed carefully, along with the underlying mechanisms. It is found that surface elastic effects significantly influence the distributions of electromechanical fields on the contact surface. Notably, the study reveals that the often-overlooked surface bending rigidity also plays a substantial role in contact conditions, exerting an influence on normal contact stress that is weaker than surface residual stress while stronger than surface membrane stiffness. Furthermore, the contact electromechanical responses exhibit strong size dependence. The contact stress distribution differs remarkably from that predicted by classical Hertz theory when the indenter size reduces to 0.1 μm, and decreases as the indenter size diminishes. The results provide some theoretical insights on optimizing performance of electronic devices based on piezoelectric materials.