A simplified multiscale magneto-mechanical model for magnetic materials

•A theoretical framework is suitable for modeling both isostress and isofield magneto-mechanical effect.•This model can explain the non-monotonic effect of tensile stress on magnetization.•It can reflect the change of the magnetization of the material when the stress and the magnetic field change simultaneously. Establishing an accurate theoretical model of the influence of stress on the magnetic properties of materials is of great significance to the use of magnetic methods to detect internal stress of components. Existing magneto-mechanical effect models often use different modeling methods for variable stress and variable magnetic field load conditions, and there are limitations in the interpretation of the non-monotonic effect of tensile stress on material magnetization under variable magnetic field load condition. The simplified multiscale magneto-mechanical model proposed in this paper uses a unified method to model the magneto-mechanical effects under variable stress and variable magnetic field loads. Since the second order stress term is added to the magnetic domain free energy and the energy loss caused by pinning is considered, the proposed model can not only reflect the hysteresis characteristics of the material magnetization with magnetic field and stress, but also reflect the non-monotonic change of magnetization with tensile stress. The proposed model has the advantages of clear physical meaning, few material parameters and fast calculation. It can be applied to stress non-destructive testing, and it also contributes to better design and use of magnetic material devices.