Tensors symmetry of crystalline nonlinear piezoelectric materials

The new technologies such as the fifth generation of telecommunications (5G) and the internet of things (IoT) present a set of demanding technical requirements at device level that can be reached through devices based on piezoelectric materials using nonlinear effects to increase their performance. However, in the literature can not be found a physics formulation for the unified nonlinear effects of these materials that allow an easy implementation in FEM simulators. Thus, in this work we use the stress-charge formulation to obtain the transformation laws, the unique components of the higher order tensors and the equations of state, which unify the nonlinear phenomena of the piezoelectric effect reported experimentally and, which can be used to increase the performance of the devices and extend the range of applications based on these materials. In addition, the methodology for their implementation on the main FEM simulators is presented.