# 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.

## Hysteresis modeling

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, two static hysteresis models exist in Flux for soft materials, the available models are the following ones:

## 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

(top left and bottom left quadrants)

Anhysteretic curve

## 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. If the magnetic device produces some demgnetization over the magnets because of the magnetic field, the following model:

may take in account the demagntization modeling during the solving process.

## Consequence for the magnetic losses computation

The hysteresis modeling allows evaluating precisely the iron and the hysteretic losses, for more informations, see this chapter.