A Dynamic Hysteresis Constitutive Relation for Giant Magnetostrictive Materials

Giant Magnetostrictive Materials (GMM), such as Terfenol-D materials, have complex nonlinear and hysteresis properties especially when the materials under pre-stresses are in a bias magnetic field and a time-varying excitation field. In order to totally describe the constitutive behavior of GMM, a static and nonlinear anhysteretic constitutive relation is analytically established by the thermodynamic theory and the theory of the Weiss molecular field. Having considered the energy loss of GMM arising from a time-varying field, such as AC magnetic field, a dynamic hysteresis constitutive relation for Terfenol-D materials is obtained in this paper. This constitutive relation can totally display the magnetic-elastic-thermal coupling properties and the effect of varied operating conditions on the minor magnetostriction loop of GMM, and are in good agreement with existing experimental data.