# Magnet (unidirectional): demagnetization curve (Hc, Br)

## Presentation

This model ( Nonlinear magnet described by **H _{c}** and the

**B**module ) defines a nonlinear

_{r}**B(H)**dependence with taking into account of demagnetization, wherever the curve knee is.

Main characteristics:

- the mathematical model and the direction of magnetization are dissociated
- a single material for description of several regions

## Mathematical model

In the direction of magnetization the model is a combination of a straight line and an arc tangent curve.

The corresponding mathematical formula is written:

with:

where:

- μ
_{0}is the permeability of vacuum, μ_{0}= 4 π 10^{-7}(H/m) - μ
_{rmax}is the maximal relative permeability of material - B
_{r}is the remanent flux density (T) - J
_{s}is the saturation magnetization (T)

The shape of the **B(H)** dependence in the direction of magnetization is given
in the opposite figure.

In transversal directions one can write:

B_{⊥}(H)= μ_{0}μ_{r⊥}H_{⊥}

where
μ_{r⊥} is the transverse relative permeability

## Direction of magnetization

The various possibilities provided to the user are the same ones as those presented in § Magnet (unidirectional): linear approximation.

## Demagnetization during solving

With this non-linear model, it is now possible consider the demagnetization during
solving (i.e. the degradation of a magnet's remanent magnetic flux density due to its
interaction with a demagnetizing field) by checking the specific option that is
provided during the material creation. This demagnetization model is based on a static
Preisach approach, and may be selected during the description of the **B(H)**
property of this type of material. The following remarks apply:

- Available for 2D and 3D in transient magnetic application
- In projects containing a magnet material with this option active, it is advisable to set the application to perform an initialization through a static calculation ( ).
- This model does not take in account temperature variations.

To use this model in a solved project :

- Destroy the results;
- Go in Initialization by static calculation; and select :
- Create a new material Nonlinear magnet described by Hc and Br module
- Check the option Taking in account demagnetization during solving
- Assign the material to the regions representing the magnets in the project;
- Go to to inform the direction of magnetization in the magnet
- Run the scenario.
To display the current remanent magnetic flux density of a magnet at a given time step:

- Select the desired time step;
- Create a new
**Arrows**plot, then select the magnet as support. - Then, in the formula editor, click on button
**Br Magnet**(available in the Magnetic Volume region tab) or type**BrMagnet**(without a space) in the formula field.Note: In the formula editor, a related button**Br**is available and the user could also type the corresponding formula**Br**in the formula field. Remark that these recover the original remanent magnetic flux density stored in the material description, and not the remanent magnetic flux density modified by demagnetization effects at a given time step represented by**BrMagnet**.