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

A simplifying macroscopic constitutive law for ferroelectric and ferroelast ic 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., Tsakma kis, Ch., 1997. Smart Structures and Materials 1997: Mathematics and Contro l in Smart Structures, Proceedings of SPIE, vol. 3039, 144-155), it is gene ralized to a three-dimensional tensorial formulation. The model has been im plemented in the public domain finite element code PSU of Stuttgart Univers ity. 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 el ectro-mechanical stress analysis for the mechanical boundary conditions yie lds the electro-mechanical fields as, for instance, the mechanical stress f ield. In order to verify the capabilities of our tool, a multilayer-like ac tuator geometry is analyzed. It is shown that the remanent polarization rem aining after poling gives rise to a non-vanishing distribution of the elect ric potential even it is reduced to zero at the electrodes. Concerning the residual stresses present after poling, a tensile stress field perpendicula r 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 conclu ded that our finite element tool is suitable for studying the influence of geometry and material parameters on the stresses in critical regions of pie zoceramic devices. (C) 2000 Elsevier Science Ltd. All rights reserved.