# Magnet and soft materials representation

## Hysteresis and hysteresis cycle

Hysteresis is a complex phenomenon related to physically irreversible processes. It consists of the fact that, at a given moment, the value of a material property depends not only on the intrinsic properties of the material, but also on its ‘history'.

Magnetic materials are generally characterized by a hysteresis cycle . It is represented by a closed surface in the (H, B) coordinates where all points are accessible. Therefore, an infinite number of relationships between B and H exist. The figure below shows a typical configuration of a hysteresis cycle.

## Modeling hysteresis

Modeling hysteresis is a difficult problem: It is difficult to model hysteresis correctly since there is an infinite number of possible B(H) curves, as shown in the figure above.

That is why in Flux, the majority of models don't take into account the hysteresis. Currently, a static hysteresis model exists in Flux for soft materials. The works on dynamic hysteresis models are in progress.

## … in Flux

In Flux, for most of models, the B(H) dependence is a univocal relationship: one value of B corresponds to one value of H and vice versa.

## How to choose a univocal relationship?

As described above, the hysteretic behavior must be approximated by univocal characteristics.

This approximation can be accomplished in various ways, taking into consideration the type of material and its utilization.

The table below presents the univocal dependencies currently utilized by Flux for the modeling of hard and soft magnetic materials.

Hard magnetic material Soft magnetic material

Demagnetization curve

Intermediate curve

( ≈ curve of 1 st magnetization)

## Explanation

With this approximation, the soft magnetic materials are modeled by their curve of first magnetization, which is justified by the very low value of the coercive magnetic field strength.

Permanent magnets are modeled by the demagnetization curve of their major hysteresis cycle, but one must check a posterior i that the magnetic state remains within the reversibility (upper) zone of the cycle, and that there is no magnet demagnetization during the device operation.

## Consequence for the magnetic losses computation

The hysteresis modeling allows evaluating precisely the iron losses.

But, the most of material models in Flux don't take into account the hysteresis.

Neglecting the hysteresis cycle is needed for simplifying the numerical simulation, but it is also accepted on the hypothesis that hysteresis does not essentially modify the distribution of magnetic flux within the electrotechnical device.

It is precisely this hypothesis that certain authors utilize in order to calculate the losses in electrical machines, even if electric motors sheets present non-negligible hysteretic characteristics.

The finite element computation of magnetic flux density repartition is usually carried out in magnetostatics, and then the magnetic losses are evaluated by means of theoretical or experimental formulas starting from the distribution of the magnetic flux density.