This paper addresses the development of a free energy model for magnetostrictive transducers operating in hysteretic and nonlinear regimes. Such models are required both for material and system characterization and for model-based control design. The model is constructed in two steps. In the first, Helmholtz and Gibbs free energy relations are constructed for homogeneous materials with constant internal fields. In the second step, the effects of material nonhomogeneities and nonconstant effective fields are incorporated through the construction of appropriate stochastic distributions. Properties of the model are illustrated through comparison and prediction of data collected from a typical Terfenol-D transducer.i Report Documentation PageForm 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.

This paper addresses the modeling of strains generated by magnetostrictive transducers in response to applied magnetic elds. The measured strains are dependent upon both the rotation of moments within the material in response to the eld and the elastic properties of the material. The magnetic behavior is characterized through the consideration of the Jiles-Atherton mean eld theory for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. The incorporation of elastic properties is necessary to account for the dynamics of the material as it vibrates. This is modeled through force balancing which yields a wave equation with magnetostrictive inputs. The validity o f the resulting transducer model is illustrated through comparison with experimental data. i Direction of Rod Motion 000 111 Spring Washer Terfenol-D Rod Compression Bolt Permanent Magnet Wound Wire Solenoid Mass End Figure 1. Cross section of a prototypical Terfenol-D magnetostrictive transducer.

This paper addresses the development of a unified framework for quantifying hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials. Because the mechanisms which produce hysteresis vary substantially at the microscopic level, it is more natural to initiate model development at the mesoscopic, or lattice, level where the materials share common energy properties along with analogous domain structures. In the first step of the model development, Helmholtz and Gibbs energy relations are combined with Boltzmann theory to construct mesoscopic models which quantify the local average polarization, magnetization and strains in ferroelectric, ferromagnetic and ferroelastic materials. In the second step of the development, stochastic homogenization techniques are invoked to construct unified macroscopic models for nonhomogeneous, polycrystalline compounds exhibiting nonuniform effective fields. The combination of energy analysis and homogenization techniques produces low-order models in which a number of parameters can be correlated with physical attributes of measured data. Furthermore, the development of a unified modeling framework applicable to a broad range of ferroic compounds facilitates material characterization, transducer development, and model-based control design. Attributes of the models are illustrated through comparison with piezoceramic, magnetostrictive and shape memory alloy data and prediction of material behavior. Keywords: Ferroic materials, unified models, hysteresis, constitutive nonlinearities i Report Documentation PageForm 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.

In this paper we develop a macroscopic framework quantifying the hysteresis and constitutive nonlinearities inherent to ferromagnetic materials. In the first step of the development, we construct Helmholtz and Gibbs energy relations at the mesoscopic or lattice level based on the assumption that magnetic moments or spins are restricted to two orientations. Direct minimization of the Gibbs energy yields local average magnetization relations appropriate for operating regimes in which relaxation mechanisms are negligible whereas the balance of the Gibbs and relative thermal energies through Boltzmann principles provides local models which incorporate mechanisms such as thermal after-effects. To construct macroscopic relations that incorporate material nonhomogeneities, polycrystallinity, and variable effective fields, we employ stochastic homogenization techniques based on the assumption that parameters such as local coercive and interaction fields are manifestations of underlying distributions. The resulting framework quantifies in a natural manner the anhysteretic magnetization provided by decaying AC fields and guarantees the closure of biased minor loops once transient accommodation and after-effects are complete. Furthermore, noncongruency is achieved with certain choices for the energy functionals. Hence the framework provides an energy basis for certain extended Preisach models and the relation of the framework to several macroscopic hysteresis models is detailed. The behavior of both the nonlinear anhysteretic relations and full hysteresis model are validated through comparison with experimental steel and nickel data.i Report Documentation PageForm 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.

This paper addresses the modeling of hysteresis in magnetostrictive transducers. This is considered in the context of control applications which require an accurate characterization of the relation between input currents and strains output by the transducer. This relation typically exhibits signi cant nonlinearities and hysteresis due to inherent properties of magnetostrictive materials. The characterization considered here is based upon the Jiles-Atherton mean eld model for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. As demonstrated through comparison with experimental data, the magnetization model very adequately quanti es both major and minor loops under various operating conditions. The combined model can then be used to accurately characterize output strains at moderate drive levels. The advantages to this model lie in the small number (six) of required parameters and the exibility it exhibits in a variety of operating conditions.