Opera-2d Magnetization and Hysteresis Module

The Opera (de-)magnetization and hysteresis module has been developed specifically to model both the magnetization process for hard magnetic materials, and the hysteresis behaviour of soft magnetic materials. Simulate ferromagnetic hysteresis with realistic demands on resource, material data and with good approximation to physical behaviour with the Hysteresis material model. Model the magnetization process for hard magnetic materials and remnant magnetization vector when the process is complete. Further demagnetization and remagnetization of the sample in situ can also be simulated.

Hysteretic Material

Ferromagnetic hysteresis is important in many areas of electrical engineering design both as a useful and also as an unwanted phenomenon. The ability to model hysteresis can be used for example to minimize hysteresis losses in transformers and electrical machines. In the Opera-2d suite a semi-empirical method for modelling hysteresis has been developed alongside industrial partners. The magnetic behaviour is considered as a trajectory B(H). The trajectory is based on a measured major symmetric loop that is supplied by the user. This data may be easily obtained from measurements or published data-sheets, and imported into Opera as a magnetic characteristic table. The Opera hysteresis model includes the issues of nested minor loops and ‘wiping out’ of minor loops, which occurs when the trajectory goes through an earlier turning point. Moreover, the model recognises oscillating fields and minimises the storage of turning points. Transition to saturation is treated automatically, allowing the simulation to overcome any limitations in the user’s data. Hysteretic material models are available in all Opera-2d transient electromagnetic simulations – dynamics, rotating and linear motion and demagnetisation. Opera-2d includes the ability to model hysteretic materials under transient conditions using a B(H) trajectory-following algorithm. Hysteretic materials can be used in conjunction with the transient and motion electromagnetic solvers. The user needs to supply data for only the major hysteresis loop. The algorithm uses a reconstruction technique to determine minor loops and turning points of the trajectory and to erase turning points when the magnetization of a material exceeds the previous excursion. The algorithm also correctly transfers to the saturated material curve beyond the end of the user data, in the same way as for anhysteretic materials in Opera-2d.

Hysteresis losses

During a transient calculation using this capability, the loss due to hysteresis in the hysteretic material is calculated. At each output time, the energy density (the sum of the stored and dissipated energy since the beginning of the transient simulation) can be displayed.

Magnetization and Demagnetization of Permanent Magnets

With hard magnetic materials, the simulation records the progress of the material magnetization along the virgin characteristic, until the magnetizing field starts to reduce. Secondary ‘demagnetization’ characteristics are then used to determine the remnant magnetization vector when the magnetization process is complete. In both the magnetization and demagnetization processes, the effect of eddy currents and circuit transients are captured. The result is a magnetized sample, where the magnetization distribution is correctly defined. This can then be used in other simulations to model the performance of the magnetized sample in its designated application (eg. an electrical machine). During the simulation of the application further demagnetization and remagnetization of the sample in the application device due to the presence of current sources can also be modelled. The Opera-2d (de-)magnetization analysis module (DEMAG) can be used to compute the magnetization of permanent magnet materials by time varying electromagnetic fields in three dimensions including the effects of eddy currents.


During the magnetization process, the maximum value of the flux density in each element is monitored and stored.


During demagnetization, the values of the pre-stored values determine which demagnetization (second quadrant) curve each element follows and its direction of magnetization. Again the flux density in each element is monitored and the minimum values are stored in variables. The values can then be transferred to the standard Opera transient solvers. In such a simulation where the applied field from current sources etc are opposing the magnet’s field, the variables will show the operating point of the magnet. In a transient simulation, they will show the lowest operating point that was reached during the transient event.


If the flux density in element moves into the irreversible part of the 2nd (or 3rd) quadrant curve, i.e. goes beyond the knee of the curve, and the demagnetizing field is then subsequently removed, the remagnetization curve is a straight line defined by its slope (the recoil permeability) and the relevant point on the demagnetization curve. Demagnetization in service can be modelled. The minimum field will be tracked and updated during subsequent simulations, and the appropriate demagnetization curve or recoil permeability will be used.