Enhanced finite element scheme for non-linear piezoelectricity

According to a thermodynamically consistent model, we decompose the physical quantities dielectric displacement and mechanical strain into a reversible and an irreversible part. Therewith, we set the irreversible part of the dielectric displacement equal to the electric polarization. The reversible parts of mechanical strain and dielectric displacement are further described by the linear piezoelectric constitutive law. The irreversible polarization is computed from the history of the driving electric field by a Preisach hysteresis operator. Furthermore, the entries of the piezoelectric modulus tensor are assumed to be a function of the irreversible dielectric polarization. This enhanced model for non-linear piezoelectricity has been recently implemented into our Finite Element (FE) software environment. We have applied our FE scheme to the numerical computation of the dynamic behavior of a piezoelectric stack actuator. The obtained results compare well to measured data.