Phenomenological modelling of the non-linear behavior of ferroelectric materials

Piezoceramics exhibit an electro-mechanical coupling which enables them to produce a proportional electric charge when subjected to a mechanical stress or to deform in presence of an electric field. In the case of more severe loading, the response is no longer linear and it is characterized by the switching of uniformly polarised domains. Thus, ferroelectricity and ferroelasticity induce irreversible polarisation and strain. This non-linear effect is desired for present day's applications since greater values of displacements could be obtained. However, the complexity of the coupling has to be overcome to design structures involving such materials and some tools like finite element codes taking into account this specific behaviour are needed for this purpose. A phenomenological law for ferroelectric and ferroelastic piezoceramics is presented. Internal variables are introduced and their evolution laws are provided by two loading surfaces. The characteristic hysteresis are obtained on the basis of this model.