Ampère’s Law
The Ampère’s Law node adds Ampère’s law for the magnetic field and provides an interface for defining the constitutive relation and its associated properties as well as electric properties.
Material Type
The Material type setting decides how materials behave and how material properties are interpreted when the mesh is deformed. Select Solid for materials whose properties change as functions of material strain, material orientation, and other variables evaluated in a material reference configuration (material frame). Select Nonsolid for materials whose properties are defined only as functions of the current local state at each point in the spatial frame, and for which no unique material reference configuration can be defined. Select From material to pick up the corresponding setting from the domain material on each domain.
Constitutive Relation B-H
Specify the constitutive relation that describes the macroscopic properties of the medium (relating the magnetic flux density B and the magnetic field H) and the applicable material properties, such as the relative permeability.
The equation for the selected constitutive relation displays under the list. For all options, the default uses values From material, or select User defined to enter a different value or expression.
Select a Magnetization modelRelative permeability (the default), B-H curve, Magnetic losses, Remanent flux density, Magnetization, or Effective B-H curve.
Relative Permeability
Select Relative permeability μr (dimensionless) to use the constitutive relation B = μ0μrH. For User defined select Isotropic, Diagonal, Symmetric, or Full and enter values or expressions in the field or matrix.
B-H Curve
Select B-H curve |H| (SI unit: A/m) to use a curve that relates magnetic flux density B and the magnetic field H as |H| = f(|B|).
The Magnetic field norm and Magnetic coenergy density settings can take the values From material or User defined.
When User defined is selected, specify a user-defined expression for the magnetic field norm. The direction of the magnetic field is taken to be the same as the direction of the magnetic flux density at each point.
Magnetic Losses
Select Magnetic losses μ and μ(dimensionless) to describe the relative permeability as a complex-valued quantity: μr = μ′ − iμ″, where μ and μ are the real and imaginary parts, respectively. Note that the time-harmonic Sign Convention requires a lossy material to have a positive material parameter μ″ (see Modeling Losses in the Frequency Domain).
Remanent Flux Density
Select Remanent flux density Br (SI unit: T) to use the constitutive relation B = μ0μrecH + Br, where μrec and Br are the recoil permeability and the remanent flux density respectively (the flux density when no magnetic field is present). The recoil permeability μrec is very similar to the relative permeability, and is valid as long as the magnet is subjected to normal operating conditions (it is only valid within the linear region close to the vertical axis H = 0). Br is given by taking the remanent flux density norm (typically, provided by the material) and multiplying it with a normalized direction field specified in the physics: Br = ||Br|| e/||e||.
The default recoil permeability μrec (dimensionless) uses values From material. For User defined, select Isotropic, Diagonal, Symmetric, or Full based on the characteristics of the recoil permeability and enter another value or expression in the field or matrix.
The remanent flux density norm ||Br|| is taken From material by default. The AC/DC branch in the material library contains a number of hard magnetic materials specifically for this purpose. Alternatively, choose User defined, and specify your own expression.
Enter x and y components for the Remanent flux direction e.
Magnetization
Select Magnetization M (SI unit: A/m) to use the constitutive relation B = μ0H + μ0M. Enter x and y components.
Effective B-H Curve
Select Effective B-H curve |H|eff (SI unit: A/m) to use an effective curve that provides the local linearized relation between the magnetic flux density B and the magnetic field H in time-harmonic problems.
External Material
Select External material to use a curve that relates magnetic flux density B and the magnetic field H as |H| = f(|B|) according to an externally coded function.
Specify the External material to use (from the Materials node under Global Definitions). This setting allows using material models or constitutive relations defined in an external library. See Working with External Materials for more information.
Constitutive Relation Jc-E
This section is described for the Current Conservation feature.
Constitutive Relation D-E
The default Relative permittivity εr (dimensionless) for the media is used From material and defined on the shell domain. For User defined, select Isotropic, Diagonal, Symmetric, or Full based on the characteristics of the permittivity and then enter values or expressions in the field or matrix.