Finite element analysis of piezoceramic components taking into account ferroelectric hysteresis behavior

A simplifying macroscopic constitutive law for ferroelectric and ferroelastic hysteresis e€ects of piezoceramics is presented. After summarizing the uniaxial formulation motivated elsewhere (Kamlah, M., Tsakmakis, C., 1999. Int. J. Solids Struct. 36, 669±695; Kamlah, M., Bohle, U., Munz, D., Tsakmakis, Ch., 1997. Smart Structures and Materials 1997: Mathematics and Control in Smart Structures, Proceedings of SPIE, vol. 3039, 144±155), it is generalized to a three-dimensional tensorial formulation. The model has been implemented in the public domain ®nite element code PSU of Stuttgart University. The ®nite element analysis is carried out in a two-step scheme: First the purely dielectric boundary value problem is solved for the history of the electric potential. Second, prescribing this electric potential, the electro-mechanical stress analysis for the mechanical boundary conditions yields the electro-mechanical ®elds as, for instance, the mechanical stress ®eld. In order to verify the capabilities of our tool, a multilayer-like actuator geometry is analyzed. It is shown that the remanent polarization remaining after poling gives rise to a non-vanishing distribution of the electric potential even it is reduced to zero at the electrodes. Concerning the residual stresses present after poling, a tensile stress ®eld 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 concluded that our ®nite element tool is suitable for studying the in¯uence of geometry and material parameters on the stresses in critical regions of piezoceramic devices