Characterization of Terfenol-D and Comparison With Predictions of a Thermodynamically Consistent Two-Input, Two-Output Model of Hysteresis

Since its discovery more than 40 years ago, Terfenol-D has promised much but has not yet been fully exploited in applications. The main reason for this is that it shows significant hysteresis and other nonlinearities, such as saturation, which need to be modeled correctly in order to maximize the application potential. In this article, we focus on the characterization of a Terfenol-D sample with the intention of developing a predictive two-input (magnetic field and stress) and two-output (magnetic flux density and strain) model of magnetostriction that exhibits hysteresis and saturation and is compatible with the laws of thermodynamics. Compatibility with thermodynamics is essential to ensure that numerical simulations do not exhibit unphysical behavior. The model is based on the Preisach hysteresis operator and its storage function and may be interpreted as a two-input, two-output neural net with elementary hysteresis operators as the neurons. In order to estimate the parameters, it is necessary to collect data over a wide range of magnetic fields (-300 to 300 kA/m) and compressive stresses (up to 60 MPa). Using the rate-independent memory evolution properties of the Preisach operator, we split the parameter estimation problem into three numerically well-conditioned, linear least squares problems with constraints. We show that the model is able to fit experimental data for strain and magnetization over a wide range of magnetic fields and stress.