@article{ball_smith_kim_seelecke_2007, title={A stress-dependent hysteresis model for ferroelectric materials}, volume={18}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X07070937}, abstractNote={ This article addresses the development of a homogenized energy model which characterizes 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. }, number={1}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Ball, Brian L. and Smith, Ralph C. and Kim, Sang-Joo and Seelecke, Stefan}, year={2007}, month={Jan}, pages={69–88} }
 @article{seelecke_kim_ball_smith_2005, title={A rate-dependent two-dimensional free energy model for ferroelectric single crystals}, volume={17}, ISSN={["1432-0959"]}, DOI={10.1007/s00161-005-0207-7}, abstractNote={The one-dimensional free energy model for ferroelectric materials developed by Smith et al. [29–31] 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 BaTiO3 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.}, number={4}, journal={CONTINUUM MECHANICS AND THERMODYNAMICS}, author={Seelecke, S and Kim, SJ and Ball, BL and Smith, RC}, year={2005}, month={Dec}, pages={337–350} }