In [1] we proposed an approach of formalizing piezo-bar actuator dynamics models in the engineer languages. The proposed models were based on a first approximation considering that the piezo-material is linear. However, as soon as the solicitations increase one will realize that this assumption is no longer valid because non-linearities are observed. And these phenomena can seriously affect the device performances. That is why several works are conducted in order to well understand the phenomena and eventually propose means of controlling them. So, above of all we shall give in this paper an overview of existing approaches. As said in [2], all these non-linearities in piezoelectric materials are well analyzed but mostly in the framework of the fundamental physics of crystals and thermodynamics and these descriptions are extremely difficult to handle. Therefore is important to make a bridge between the fundamental studies of piezoelectric materials and classical engineering field. It is actually the purpose of this paper. We will see that due to the complexity of the phenomena and especially numerical and algebraic troubles, some simplifications could be necessary.

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