A quasi-three-dimensional approach to modeling and analysis of a constrained piezoelectric thin film

This work presents a semi-analytical quasi-three-dimensional model of a piezoelectric thin film intended to describe the performance of the constrained thin film through intricate analysis and numerical simulations. The model is based on 3D electromechanical continuum mechanics of the piezoelctric film, with due consideration of the restriction on thickness of the film to be categorized as a thin film. This model requires the displacement variation on the surface of the thin film as input, and this can normally be extracted from the analysis of the host structure using different numerical techniques, e.g., finite element, finite difference, and boundary element models. The performance studies are reported in terms of the potential difference and capacitance of the film. The model is, first, validated by comparing the results for the simple case with the existing model. Analyses are also performed for different displacement variations that are normally encountered in structural mechanics problems. In order to demonstrate its usefulness in structural health monitoring problems, the behavior of the thin film under modes I and II loading for a through crack in the structure is also studied. Numerical simulations are conducted with Polyvinylidine Difluoride films, although the model also works well for other piezoelectric materials, such as Lead Zirconate Titanate.