American Institute of Aeronautics and Astronautics 1 Finite element modeling of piezoelectric materials under electromechanical loading Arunachalakasi Arockiarajan * and Buelent Delibas  Chair of Applied Mechanics, University of Kaiserslautern, Kaiserslautern, 67663, Germany Andreas Menzel  Chair of Applied Mechanics, University of Kaiserslautern, Kaiserslautern, 67663, Germany and Wolfgang Seemann § Institute for Technical Mechanics, University of Karlsruhe, Karlsruhe, 76128, Germany Nowadays, there are increasing interests in piezoelectric and ferroelectric materials which are especially used in scientific and engineering applications. Though these materials have good characteristics, the behavior for large loadings can only be described by nonlinear relations which limit their usage in high performance applications. Domain switching (ferroelastic or ferroelectric) is the main reason for the nonlinearity of ferroelectric materials. External excessive electromechanical loads (mechanical stress and electric field) are driving forces for the domain switching process. The nonlinear behavior of piezoelectric materials subjected to electromechanical loading is simulated by a theoretical micromechanical approach using a 3-D finite element model. The model accounts for differently oriented grains. The dipole directions of the grains in the simulation model are randomly distributed. This is obtained by three equally distributed Euler angles for each grain at virgin state. Uni-axial, quasi-static loading is applied in the simulations. The behavior of piezoelectric materials subject to electromechanical loading is then investigated for a constant compressive stress and a cyclic electric potential at the electrodes. The response of the macroscopic behavior of the bulk ceramic is predicted by averaging the response of all individual grains. It is assumed that a crystal switches if the reduction in free energy of the grain exceeds a critical energy barrier. Due to intergranular effects domain switching may occur in reality even for those grains, for which the critical energy level is not reached. This effect is modeled by introducing a probability for domain switching, which depends on the ratio of the actual energy level to the critical energy level. Different functions may also be used to describe the probability. In the present work, however we restrict to polynomials. Using these probability functions it is possible to model the nonlinearity even in a small electromechanical loading range. The effect of different orders of the polynomial for the probability function and different material parameters are also analyzed. The results of the simulations are compared with experimental data taken from the literature. In addition to this, rate dependent properties of piezoceramics are investigated by implementing various frequencies of cyclic electrical loading. The frequency dependence of the behavior is obtained by using linear kinetics theory. In this approach the nucleation and propagation of the domain wall during domain switching is modeled. In the simulations different amplitudes of alternating loading are applied with various frequencies in order to understand the macroscopic behavior of piezoelectric and ferroelectric materials. Important parameters are the coercive field and the remnant polarization and strain characterization under various loading situations. The response of the material to the applied loading is * Research Assistant, Chair of Applied Mechanics, Gottlieb Daimler str.44, (SS).  Research Assistant, Chair of Applied Mechanics, Gottlieb Daimler str.44.  Post doc. fellowship, Chair of Applied Mechanics, Gottlieb Daimler str.44. § Professor, Institute for Engineering Mechanics, Kaiser Str.12. 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 18 - 21 April 2005, Austin, Texas AIAA 2005-1909 Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.