Evolution of nonlinear magneto-elastic constitutive laws in ferromagnetic materials: A comprehensive review

An extensive growth in the application of ferromagnetic materials require a firm theoretical understanding of the material behavior to accomplish accurate model prediction. The aim of this review article is to capture the evolutionary journey of the nonlinear magnetoelastic constitutive laws, spanning since the mid-twentieth century. This review discusses the prominent proposed constitutive models based either on physical or phenomenological considerations, by classifying them into two categories, the anhysteretic and the hysteretic, which further incorporates the effect of magnetic field, stress, temperature, and plastic deformation on the ferromagnetic material behavior. The respective advantages and limitations offered by the various classes of proposed approaches in the form of Jiles–Atherton model, Armstrong model, Zheng–Liu model, Preisach model, Stoner–Wohlfarth model, multiscale model, Play model, Plasticity based model, Continuum based model have been summarized. Finally, a holistic outlook is presented portraying the state of the art and avenues for improvement that future research might hold regarding the refinement of the available nonlinear magnetoelastic constitutive laws.