The linear behavior of piezoelectric materials is well known from a century ago, but also, the non-linear behavior for these material have found a novel way of applications. Currently, the new technologies as the fifth generation of telecommunications (5G) and Internet of Things (IoT) are demanding high requirements for the performance of the devices operating under these technologies e.g. high quality factor, high thermal efficiency and device fabrication compatibility with the standard fabrication processes for integrated circuits as CMOS, FD-SOI and FinFET. In this work, the non-linear state equations for piezoelectric effect in stress- charge formulation, the transformations laws and the high order tensors structures are presented, in order to allow an easy way to implement it on FEM simulation software. The non-linear behavior of piezoelectric materials is discussed, and taking into account the analysis done in this work, three ways to implement nonlinear effects to design tunable piezoelectric devices for 5G and IoT applications are presented.