Explicit and efficient discrete energy-averaged model for Terfenol-D

Abstract

The axis of most commercially available bulk Terfenol-D rods is misaligned with the pseudo-cubic Terfenol-D crystals. Thus, the development of efficient and accurate constitutive models for Terfenol-D has traditionally been challenging. This study presents a fully coupled and efficient discrete energy-averaged model that describes the nonlinear magnetostrictive behavior of Terfenol-D. The model is built on the basis of the Stoner-Wohlfarth particle approximation, where the anhysteresis bulk response of magnetostrictive materials is considered as a weighted sum of local magnetic domain responses and the material hysteresis is defined by an evolution function for the weights. The local responses are explicitly calculated through minimizing the free energy of individual magnetic domains; the weights, also known as the domain volume fractions, are described by an energy-based Boltzmann distribution. Advanced computation algorithms are developed to further improve the model efficiency. The model is used to interpret magnetic flux density and strain measurements from multiple [112]-oriented Terfenol-D rods. According to the modeling results, the explicit constitutive model developed in this study is three to five times faster than the previous implicit discrete energy-averaged model while preserving accuracy.