Nonlinear piezoelectric materials are raised as a great replacement for devices that require low power consumption, high sensitivity, and accurate transduction, fitting with the demanding requirements of new technologies such as the Fifth-Generation of telecommunications (5G), the Internet of Things (IoT), and modern radio frequency (RF) applications. In this work, the state equations that correctly predict the nonlinear piezoelectric phenomena observed experimentally are presented. Furthermore, we developed a fast methodology to implement the state equations in the main FEM simulation software, allowing an easy design and characterization of this type of device, as the symmetry structures for high-order tensors are shown and explained. The operation regime of each high-order tensor is discussed and connected with the main nonlinear phenomena reported in the literature. Finally, to demonstrate our theoretical deductions, we used the experimental measurements, which presented the nonlinear effects, which were reproduced through simulations, obtaining maximum percent errors for the effective elasticity constants, relative effective permittivity, and resonance frequencies of 0.79%, 2.9%, and 0.3%, respectively, giving a proof of the potential of the nonlinear state equations presented for the unifying of all nonlinear phenomena observed in the piezoelectric devices.
Keywords: high-order tensors; nonlinear piezoelectric applications; nonlinear piezoelectric devices; stress–charge formulation; tensor symmetry structure; tunable piezoelectric devices.