Three-dimensional constitutive equations of ferromagnetic materials with magnetoelastic coupling: Determination of elastic coefficients under magnetic field

This paper determines the elastic coefficients in the constitutive equations of typical ferromagnetic materials. The constitutive equations are given by rate-type equations for the magnetization and the strain expressed in terms of the magnetic field and the stress. The authors have shown that the constitutive equations can describe the stress-dependent hysteretic magnetization curve, the stress magnetization effects, the stress-dependent magnetostriction curve, etc. They have determined the coefficients except the elastic coefficients as functions of the magnetization and the stress for typical ferromagnetic materials. In this paper, we attempt to obtain the elastic coefficients depending on the magnetization and the stress. To do it, applying the magnetoacoustic effect, we measure the stress–strain curves and the speeds of the longitudinal and the transverse ultrasonic waves under the magnetic field.