A stress-dependent hysteresis model for ferroelectric materials

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.