A general one-dimension nonlinear magneto-elastic coupled constitutive model for magnetostrictive materials

Da-Guang Zhang,Hao-Miao Zhou,Meng-Han Li

doi:10.1063/1.4933024

Abstract

For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.

Highlights

Magnetostrictive material is a significant functional material for energy conversion, which can convert magnetic energy into mechanical energy
The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field
The induced magnetization and strain are along axial direction for pre-stress and external magnetic field applied along axial direction, the constitutive model describing the relationship between stress σ, strain ε, magnetic field H and magnetization M can be simplified to a one-dimension model

Summary

INTRODUCTION

Magnetostrictive material is a significant functional material for energy conversion, which can convert magnetic energy into mechanical energy. As can be seen from the above analysis, pre-stress has a similar effect on magnetostrictive strain and magnetization of different magnetostrictive materials; establishing a general constitutive relation for magnetostrictive materials is very necessary. Zheng et al.[19] divided the elastic strain produced by pre-stress into nonlinear part associated with the domain rotation and linear part independent of domain rotation, and built Zheng-Liu model for Terfenol-D rod which first achieves an accurate prediction of magnetostrictive strain under different pre-stresses in the region of low, moderate and high field. Based on Zheng-Liu model, taking the influence of temperature on magnetostrictive effect into consideration, Sun et al.[20] established a constitutive model to describe the magneto-thermo-mechanical coupling under different magnetic fields, pre-stresses, and temperatures. In order to overcome the other shortcoming that explicit magnetization relationship is inconvenience to get for the existence of the inverse function in Zheng-Liu model, a new nonlinear magnetization function is selected in the model

MODELING

QUANTITATIVE DISCUSSION

CONCLUSION