The Homogenized Energy Model (HEM) for Characterizing Polarization and Strains in Hysteretic Ferroelectric Materials: Implementation Algorithms and Data-Driven Parameter Estimation Techniques

Abstract

Ferroelectric materials, such as PZT, PLZT, PMN and BaTiO 3 , provide unique actuator and sensor capabilities for applications including nanopositioning, high speed valves and fuel injectors, camera focusing and shutter mechanisms, ultrasonic devices for biomedical imaging and treatment, and energy harvesting devices. However, to achieve the full potential of the materials, it is necessary to develop and employ models that quantify the creep, rate-dependent hysteresis, and constitutive nonlinearities that are intrinsic to the materials due to their domain structure. The success of models requires that they be highly efficient to implement since real-time applications can require kHz to MHz rates. The calibration of models for specific materials, devices, and applications, requires efficient and robust parameter estimation algorithms. Finally, control designs can be facilitated by models that admit efficient and robust approximate inversion. The homogenized energy model (HEM) is a multiscale, micromechanical framework that quantifies a range of hysteretic phenomena intrinsic to ferroelectric, ferromagnetic and ferroelastic materials. In this paper, we present highly efficient implementation and parameter estimation algorithms for the ferroelectric model. This includes techniques to construct analytic Jacobians and data-driven algorithms to determine initial parameter estimates to facilitate subsequent optimization. The efficiency of these algorithms facilitates material and device characterization and provides the basis for constructing efficient and robust inverse algorithms for model-based control design. The model implementation, calibration, and validation are illustrated using rate-dependent PZT data and single crystal BaTiO 3 data. i Report Documentation Page Form Approved OMB No. 0704-0188 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.

Sliding mode control based on an inverse compensator design for hysteretic smart systems

“…Recent work [6], [14] incorporates the effects of 90 • switching to model both polarization and strain responses to applied electric fields and stresses. The consideration of 90 • switching in the model is important for accurately modeling strain, since 90 • switching is one of the primary strainproducing mechanisms in ferroelectric materials.…”

“…Efficient algorithms for computing the evolution of the phase fractions for the 180 • switching model are discussed in [3], which are equally applicable to the 90 • model used in this work. A full discussion of the model implementation is available in [6].…”

“…We briefly discuss details of the implementation. A more thorough description of numerical methods for implementing the homogenized energy model is available in [6].…”

Data-driven techniques to estimate parameters in the homogenized energy model for shape memory alloys

“…In the second method, the parameters are incorporated into the optimization process with the density functions. Similar techniques for estimating parameters for ferroelectric and ferromagnetic models are presented in [11,12].…”

Modeling and Bayesian Parameter Estimation for Shape Memory Alloy Bending Actuators

“…The homogenized energy model (HEM) is used, which has been applied to various smart materials. [11][12][13][14][15][16][17][18][19][20] The approach to quantify uncertainty is described, including optimization of model parameters and the Markov Chain Monte Carlo method used here. Finally, the results are presented.…”