Nonlinear Applications, State Equations and Simulations for Piezoelectric Materials

The nonlinear effects of piezoelectric materials can be used in the 5G and IoT scope, and considering that the most general problems have not analytic solution, the FEM simulations are a fundamental design tool. In this work, we present the stress-charge formulation for nonlinear piezoelectric materials, such it is compatible and has an easy way to implement for the most commonly simulations tools used in industry and research level. Also, we present the simulations results for the variable capacitance and resonance frequency shift nonlinear phenomena, having a good fitting with the recent and important experimental results. The value of the components of the nonlinear tensors founded for the simulations were g 333 = −80N/V m and $q_{331}^r = q_{333}^r = - 1600$. The average percent errors obtained for simulations of resonance frequency shift was 0.32%, and for the variable capacitance was 0.069%.