Magnetoelastic Vector Hysteresis Modeling for Electromagnetic Devices: A Combination of a Multiscale Model With the Energy-Based Hysteresis Framework

In this work, the simplified multiscale model (SMSM) is incorporated into the energy-based (EB) quasi-static vector hysteresis model to represent the anhysteretic part of the material behavior. This approach enables the inclusion of effects such as mechanical stress, magnetostriction, material anisotropy, and crystallographic texture. By integrating the anhysteretic model into the EB framework, it becomes possible to account for dissipative effects (in our case, domain wall pinning) while utilizing detailed material information. To solve the EB model in conjunction with the SMSM, two approaches are pursued: a numerical optimization of a free energy functional and an explicit approximate variant, known as the vector play model (VPM). Both methods are compared in terms of computational performance, and the differences in results are demonstrated through the simulation of the cross section of an electric machine. Furthermore, the local as well as global behavior is investigated. It is shown that in an electrical machine configuration, the VPM provides a very satisfactory approximation to both local and global responses, together with a reduced computation time compared to the EB model. In the provided application case, it is shown that a shrink-fitting operation can lead to a 30% increase in the overall hysteresis losses.