This paper addresses the development of homogenized energy models which characterize the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. In the first step of the development, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 • and 180 • dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. In the final step of the development, stochastic homogenization techniques are employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds. Attributes and limitations of the characterization framework are illustrated through comparison with experimental PLZT data. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

This paper addresses the development of homogenized energy models which characterize the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. In the first step of the development, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 • and 180 • dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. In the final step of the development, stochastic homogenization techniques are employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds. Attributes and limitations of the characterization framework are illustrated through comparison with experimental PLZT data. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

Abstract. The one-dimensional free energy model for ferroelectric materials developed by is generalized to two dimensions. The two-dimensional free energy potential proposed in this paper consists of four energy wells that correspond to four variants of the material. The wells are separated by four saddle points, representing the barriers for 90 • -switching processes, and a local maximum, across which 180 • -switching processes take place. The free energy potential is combined with evolution equations for the variant fractions based on the theory of thermally activated processes. The model is compared to recent measurements on BaTiO 3 single crystals by Burcsu et al. [8], and predicitions are made concerning the response to the application of in-plane multi-axial electric fields at various frequencies and loading directions. The kinetics of the 90 • -and 180 • -switching processes are discussed in detail.

Pre-stressed curved actuators consist of a piezoelectric ceramic (lead zirconate titanate or PZT) sandwiched between various substrates and other top layers. The substrates used in this study are stainless steel, and fiberglass. The top layers are made up of aluminum and carbon. Due to their enhanced strain capabilities, these pre-stressed piezoelectric devices are of interest in a variety of aerospace applications. Their performance as a function of electric field, temperature and frequency is needed in order to optimize their operation. During the processing steps, a mismatch between the properties of the various layers leads to pre-stressing of the PZT layer. These internal stresses, combined with restricted lateral motion, are shown to enhance the axial displacement. The goal is to gain an understanding of the resulting piezoelectric behavior over a range of voltages, and frequencies, for unloaded conditions. To quantify the relationship between the state of stress in the ceramic and the overall performance, a physics-based model is developed incorporating both thermo elastic relations and ferroelectric domain theory. The model predicts displacements based on the geometry and physical characteristics of the actuator components. The accuracy of the model and associated numerical method is demonstrated through comparison with experimental data for various input voltages, and boundary conditions.

This paper develops a macroscopic polarization switching model which characterizes the ferroelastic switching mechanisms inherent to lead zirconate-titanate (PZT) in a manner suitable for subsequent transducer and control design. We construct Helmholtz and Gibbs energy relations at the lattice level which quantify the internal and electrostatic energy associated with 90 • and 180 • dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. Macroscopic models suitable for nonhomogeneous, polycrystalline compounds are constructed through stochastic homogenization techniques. Attributes and limitations of the model are illustrated through comparison with experimental PLZT data.