  Piezoelectricity of some materials has shown to have many applications, in
particular in energy harvesting. Due to the inherent hysteresis in the
characteristic of such materials, a number of hysteretic models have been
proposed minding the fact that hysteresis losses may influence the efficiency
of the process. However, hysteresis dissipation is accompanied with heat
production, which in turn increases the temperature of the device and may
change its physical characteristics. In this paper we propose a
phenomenological model for electromechanical coupling in piezoelectric
materials where temperature and feedback effects are taken into account. We
prove the existence of solution for the resulting PDE system and show that the
model is thermodynamically consistent. The main analytical tool is the inverse
Preisach operator with temperature-dependent density.
