# Soft and hard materials representation

## Hysteresis and hysteresis cycle

Hysteresis is a complex phenomenon related to physically irreversible processes. It consists in the fact that, at a given moment, the magnetization law describing the material 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 loop in the (H, B) coordinates where all points are accessible. Therefore, an infinite number of relationships between B and H exists. The figure below shows a typical configuration of a hysteresis cycle.

## Hysteresis modeling

Modeling hysteresis correctly is a difficult problem , since there is an infinite number of possible B(H) curves, depending on the previous values of these fields, as shown in the figure above. Moreover, hysteresis models are expensive in terms of computation time, even if they are more accurate.

## How to represent hysteresis

To limit computational resources and time, the hysteresis characteristics of materials can be approximated by univocal relationships. This emulation can be accomplished in various ways, depending on the material type and on its utilization.

The table below presents the univocal relations currently used 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 |

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

Permanent magnets (hard magnetic materials) are modeled by the demagnetization curve of their major hysteresis cycle, but one must check a posteriori that the working point remains within the reversibility (upper) zone of the cycle, and that there is no magnet demagnetization during the device operations. If in contrast the considered device produces some demagnetization over the magnets because of the magnetic field, the following model:

Magnet (unidirectional): demagnetization curve (HcB, HcJ and Br)may take in account this phenomenon during the solving process.

## Consequence for the iron losses computation

Hysteresis modeling allows evaluating precisely the hysteresis and the iron losses. For more information, see this chapter of this user guide.