# 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 to taking in account demagnetization
during solving by checking the thick that is provided for. This model is based on a
static Preisach model, and can be applied in all over the **B(H)** law of the
magnet:

- Available for 2D and 3D in magnetic transient application
- Initialization by static calculation ( )
- This model does not take in account temperature variations

To use this new model with a solved project :

- Destroy results
- Go in Initialization by static calculation and select :
- Create a new material Nonlinear magnet describes by Hc and Br module
- Check the thick Taking in account demagnetization during solving
- Assign the material to regions
- Go to
- Run the scenario
- Create a new
**isovalues**, select magnet and add**BrDemag**in the formulas field

## Example of results

- This new level of modeling can increase the computation time and the memory (ram & disk)
- Not available in 3D with the potential vector and 2D axisymmetric