On a non-linear finite element method for piezoelectric structures made of hysteretic ferroelectric ceramics

A simple macroscopic constitutive law for ferroelectric and ferroelastic hysteresis effects of piezoceramics is presented. This constitutive model has been implemented in the public domain finite element code PSU of Stuttgart University (Germany). The fully coupled electro-mechanical boundary value problem for our hysteresis model is solved by incrementation of the loading history. In order to verify the capabilities of our tool, a multilayer-like actuator geometry is analyzed. Concerning the residual stresses present after poling, a tensile stress field perpendicular to the direction of the electrodes can be found in the passive region of the actuator where so-called poling cracks are known to occur. It is the key feature of our finite element tool that it allows the consideration, in structural mechanical analyses, of such phenomena as they are induced by the remanent hysteresis properties of piezoceramics.