Piezoelectric materials exhibit hysteresis in the field-strain relation at essentially all drive levels. Furthermore, this non-linear relation is dependent upon both prestresses and dynamic stresses generated during employment of the materials. The accurate characterization of this nonlinear and hysteretic material behavior is critical for material characterization, device design, and model-based control design. In this paper, we will discuss the characterization of hysteresis using the homogenized energy model (HEM) framework. At the mesoscale, energy relations characterizing field and stress-dependent 90 and 180 degree switching are used to develop fundamental kernels or hysterons. Material and field nonhomogeneities are subsequently incorporated by assuming that certain parameters are manifestations of underlying densities. This yields a macroscopic model that accurately characterizes the fundamental material behavior yet is sufficiently efficient for optimization and control implementation. Attributes of the model will be illustrated through comparison to experimental data.

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