Modeling surface electrodes on a piezoelectric layer

This paper considers a piezoelectric ceramic layer with a surface electrode. It focuses on the effect of the layer thickness on the electrode tip fields. A closed-form solution for the electromechanical fields at the electrode tip is obtained and is expressed in terms of the applied electric field intensity factor, which can be obtained exactly for infinite layer thickness and numerically for finite layer thickness. The stress, electric displacement, and electric field are plotted to show the effect of layer thickness. It is found that the stresses and field intensities at the electrode tip can be reduced considerably by decreasing the thickness of the piezoelectric layer, confirming the previous finding. The paper also gives a solution for two identical and collinear surface electrodes. The relative distance between the electrodes is observed to have significant influence on the electromechanical field in the piezoelectric layer.