A generalized saturated capacitor model for hysteresis in piezoelectric materials

A generalized saturated capacitor (GSC) model is proposed for hysteresis in piezoelectric materials. It introduces the Weiss domains (WDs) with a negative capacitance switch (NCS) into the saturated capacitor model. The WD with NCS is modeled as a parallel network of a charge-limited capacitor and perfect one. It is further made equivalent to a series network of a voltage-limited capacitor (VLC) with negative elastance values and a perfect capacitor, which induces the GSC model to become a series network of several VLCs with positive or negative elastances. The GSC model can capture non-convex hysteresis loops and is self-invertible, namely the inverse GSC model has the same structure as the original (forward) one but differs by its parameters. The proposed model effectiveness is corroborated by the experimental data, with the maximal discrepancy not exceeding 1%.