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

Presentation

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:

with

where:

• μ₀ is the permeability of vacuum, μ₀ = 4 π 10^-7 H/m
• μ_r is the initial relative permeability of the material (at the origin)
• J_s 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 model consists in a set of three equations, one per 3D-space direction.

This model is available when the following conditions are satisfied:

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