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

A simplifying macroscopic constitutive law for ferroelectric and ferroelastic hysteresis effects 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 finite element code PSU of Stuttgart University. The finite 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 fields as, for instance, the mechanical stress field. 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 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 concluded that our finite element tool is suitable for studying the influence of geometry and material parameters on the stresses in critical regions of piezoceramic devices. (C) 2000 Elsevier Science Ltd. All rights reserved.