Isotropic / anisotropic soft material: analytic saturation curve + knee adjustment


This model defines a nonlinear B(H) dependence for an isotropic material, taking the saturation and control of the corresponding knee into consideration.

Mathematical model

This model consists, like the previous one, of a combination of a straight line and a curve. A coefficient allows for the adjustment of the knee shape in order to better approximate the experimental curve.

The corresponding mathematical formula is written as follows:



  • μ0 is the permeability of vacuum, μ0 = 4 π 10-7 H/m
  • μr is the initial relative permeability of the material (at the origin)
  • Js is the magnetic polarization at saturation T
  • a is the adjustment coefficient of the B(H) curve knee (0 < a and a < > 1)

    The smaller the coefficient, the sharper the knee is.

The shape of this B(H) model is given in the figure below.

Anisotropic material

For an anisotropic material, this linear model consists of a group of three straight lines.

This model is taken into account with the following conditions:

  • 2D applications (2D plane domain): Magneto Static / Transient magnetic
  • regions: magnetic non conducting, solid conductor