A variable kinematic model for the prediction of capacitance variations in embedded PZT sensors

This paper proposes the use of a two-dimensional refined finite element model, based on the Carrera Unified Formulation (CUF), to predict the variation in capacitance of embedded piezoelectric sensors. The accurate stress field of laminated structures with embedded sensors has been evaluated by exploiting the capabilities of refined layer-wise models. A fully coupled electro-mechanical formulation has been adopted to predict the piezoelectric response of embedded sensors. Different piezoelectric materials have been considered and a parametric analysis has been carried out including geometrical and physical parameters. The results show that the variation in capacitance is highly affected by the through-the-thickness deformations, that is, classical models cannot be used to predict this phenomenon. The variation in the capacitance value has been confirmed by experimental results proposed in the literature and can be used as a parameter for evaluating the internal stress field.