@article{braun_smith_2008, title={High Speed Model Implementation and Inversion Techniques for Ferroelectric and Ferromagnetic Transducers}, volume={19}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X07085638}, abstractNote={ Ferroelectric and ferromagnetic materials are employed as both actuators and sensors in a wide variety of applications including fluid pumps, nanopositioning stages, sonar transducers, vibration control, ultrasonic sources, and high-speed milling. They are attractive because the resulting transducers are solid-state and often very compact. However, the coupling of field to mechanical deformation, which makes these materials effective transducers, also introduces hysteresis and time-dependent behavior that must be accommodated in device designs and models before the full potential of compounds can be realized. In this article, we present highly efficient modeling techniques to characterize hysteresis and constitutive nonlinearities in ferroelectric and ferromagnetic compounds and model inversion techniques which permit subsequent linear control designs. }, number={11}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Braun, T. R. and Smith, R. C.}, year={2008}, month={Nov}, pages={1295–1310} }
 @article{smith_dapino_braun_mortensen_2006, title={A homogenized energy framework for ferromagnetic hysteresis}, volume={42}, ISSN={["1941-0069"]}, DOI={10.1109/TMAG.2006.875717}, abstractNote={This paper focuses on the development of a homogenized energy model which quantifies certain facets of the direct magnetomechanical effect. In the first step of the development, Gibbs energy analysis at the lattice level is combined with Boltzmann principles to quantify the local average magnetization as a function of input fields and stresses. A macroscopic magnetization model, which incorporates the effects of polycrystallinity, material nonhomogeneities, stress-dependent interaction fields, and stress-dependent coercive behavior, is constructed through stochastic homogenization techniques based on the tenet that local coercive and interaction fields are manifestations of underlying distributions rather than constants. The resulting framework incorporates previous ferromagnetic hysteresis theory as a special case in the absence of applied stresses. Attributes of the framework are illustrated through comparison with previously published steel and iron data}, number={7}, journal={IEEE TRANSACTIONS ON MAGNETICS}, author={Smith, Ralph C. and Dapino, Marcelo J. and Braun, Thomas R. and Mortensen, Anthony P.}, year={2006}, month={Jul}, pages={1747–1769} }
 @article{braun_smith_2006, title={Efficient implementation algorithms for homogenized energy models}, volume={18}, ISSN={["0935-1175"]}, DOI={10.1007/s00161-006-0015-8}, abstractNote={The homogenized energy framework quantifying ferroelectric and ferromagnetic hysteresis is increasingly used for comprehensive material characterization and model-based control design. For operating regimes in which thermal relaxation mechanisms and stress-dependencies are negligible, existing algorithms are sufficiently efficient to permit device optimization and the potential for real-time control implementation. In this paper, we develop algorithms employing lookup tables which permit the high speed implementation of formulations which incorporate relaxation mechanisms and electromechanical coupling. Aspects of the algorithms are illustrated through comparison with experimental data.}, number={3-4}, journal={CONTINUUM MECHANICS AND THERMODYNAMICS}, author={Braun, Thomas R. and Smith, Ralph C.}, year={2006}, month={Sep}, pages={137–155} }