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


This model ( Nonlinear magnet described by Hc and the Br module ) defines a nonlinear 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:



  • μ0 is the permeability of vacuum, μ0 = 4 π 10-7 (H/m)
  • μrmax is the maximal relative permeability of material
  • Br is the remanent flux density (T)
  • Js 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)= μ0μr⊥H

where μr⊥ 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 (Application > Transient initialization)
  • This model does not take in account temperature variations

To use this new model with a solved project :

  • Destroy results
  • Go in Application > Transient initialization and select : Initialization by static calculation
  • 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 Physics > Face regions (in 2D) or Volume regions (in 3D) > Orient material for face / volume regions
  • Run the scenario
  • Create a new isovalues, select magnet and add BrDemag in the formulas field

Example of results

Here is a surface permanent magnets motor 3D

Figure 1. Full device
For a control angle Ψ =   0   ;   π 6   ;   π 4   ;   π 3   , we can see that there is a local effect on the remanent flux density, but the repartition depends of the angle Ψ .

Figure 2. Br in the magnet
This local effect can bring some effect on global values like torque or EMF.

Figure 3. E.M.F with and without demagnetization for Ψ = π 4
  • 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