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| Sliding frictional contact of a piezoelectric half-plane considering size effects |
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Abstract Abstract With the rapid development of micro/nano electromechanical systems and piezoelectric micro-devices, the size of the devices is continuously evolving towards miniaturization. Under microscale conditions, piezoelectric materials exhibit pronounced size-dependent effects that cannot be accurately characterized by the classical piezoelectricity theory, and these effects have gradually attracted widespread attention in recent years. Based on the couple stress theory, this paper investigates the two-dimensional sliding frictional contact between a rigid insulating or conducting flat punch and a transversely isotropic piezoelectric half-plane. The theory incorporates a characteristic length parameter into the constitutive equations to account for size-dependent effects arising from material microstructure, thereby overcoming the limitations of classical piezoelectric elasticity theory in describing microscale behaviors. The surface electric potential of the conducting punch is assumed to be constant. Coulomb’s friction law is applied over the entire contact region with a constant friction coefficient. Using Fourier integral transforms, the sliding frictional contact problem is reduced to a system of Cauchy singular integral equations. The governing equations are transformed into algebraic equations through a numerical discretization method and then solved iteratively. The influences of the size parameter, friction coefficient, and total electric charge on the in-plane electric displacement, surface electric displacement, surface normal contact stress, and in-plane stress are discussed. It is found that the electroelastic fields predicted by the couple stress theory differ significantly from those obtained from the classical theory. This study provides an important theoretical foundation for the design optimization and reliability analysis of micro/nano electromechanical systems, piezoelectric sensors and actuators, and other piezoelectric devices. By taking into account the size-dependent effects caused by material microstructures, the proposed model can more accurately describe the electromechanical coupling behavior and contact response of piezoelectric materials at the microscale. This is of great significance for improving the operational stability, structural reliability, and service life of micro-devices.
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Received: 23 April 2026
Published: 30 August 2026
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2026, Vol. 47 
