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 Non-solid 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, Effective B-H curve, Hysteresis Jiles–Atherton model, Nonlinear permanent magnet, Analytic magnetization curve, or External material.
Analytic magnetization curve option is available only when the Material type is set to Solid.
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. If Effective medium is selected, a Effective Medium subnode is available from the context menu (right-click the parent node) as well as from the Physics toolbar, Attributes menu, which can specify the relative permeability of the mixture.
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.
Do not select this option in a Frequency Domain study, such as when using The Induction Heating Interface. This option is not relevant for time harmonic modeling, which assumes linear material properties.
Check your own B-H curve data using the B-H Curve Checker: Application Library path ACDC_Module/Applications/bh_curve_checker
Magnetic Losses
This option introduces a complex relative permeability and it is intended for time-harmonic (frequency domain) studies. Therefore, it is not available for The Magnetic Fields, Currents Only Interface.
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.
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, chose User defined, and specify your own expression.
Enter x and y components for the Remanent flux direction e. For 3D components, enter x, y, and z components.
Magnetization
Select Magnetization M (SI unit: A/m) to use the constitutive relation B = μ0H + μ0M. Enter x and y components. For 3D components, enter x, y, and z 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.
Generate the effective B-H curve data using the Effective Nonlinear Magnetic Curves Calculator: Application Library path ACDC_Module/Applications/effective_nonlinear_magnetic_curves
Nonlinear Permanent Magnet
Select Nonlinear permanent magnet to use a nonlinear BH-relation that is isotropic around a point in H space that is shifted by the coercive field Hc. This constitutive relation is intended for easy modeling of self-demagnetization of soft permanent magnets. It is recommended to keep all input settings at the default From material and use the example material, Nonlinear Permanent Magnet in the AC/DC material library either as is or as a template for defining customized materials. The latter is done by changing the interpolation functions defined in the material. The example material is a generic and approximate representation of AlNiCo 5.
The Direction of magnetization is the only input that normally should be entered in the physics.
Do not select this option in a Frequency Domain study, such as when using The Induction Heating Interface. This option is not relevant for time harmonic modeling, which assumes linear material properties.
Hysteresis Jiles–Atherton model
Select the Hysteresis Jiles–Atherton model to use in the constitutive relation B = μ0H + μ0M with the magnetization M (SI unit: A/m) computed from the solution of the five parameters Jiles–Atherton model. Specify the five parameters Ms, a, k, c, and α either from the material (default) or as user defined. The example material Jiles–Atherton Hysteretic Material is available in the AC/DC material library. The parameters may be tensor quantities resulting in the modeling of an anisotropic hysteretic material as shown in the application library entry:
Vector Hysteresis Modeling: Application Library path ACDC_Module/Verifications/vector_hysteresis_modeling
In stationary study, the model defaults to use Transient initialization defined by the user. Switch it to Parametric hysteresis when performing Parametric Sweep on time instants. The entry Initial Magnetization is present to set the initial values of Jiles–Atherton variables.
The Discretization section is used to choose the discretization order of Jiles–Atherton variables.
Analytic Magnetization Curve
Select this option use the constitutive relation B = μ0(H + M(H) + Mr), where Mr is the remanent magnetization (SI unit: A/m), and the magnetization vector is M(H) is calculated from the magnetic field using a nonlinear relation with possible saturation and hysteresis. This option is available only when the Material type is set to Solid.
The material is assumed to exhibit spontaneous magnetization, so that it is constituted of domains with nonzero magnetization even at zero applied field. Application of a magnetic field can rearrange the domains resulting into the net magnetization in the material. At very large applied fields, the magnetization saturates, as all domains in the material become aligned along the direction of the applied field. Domain wall interactions can also lead to a significant hysteresis in the magnetization process.
All domains have magnetization of the same magnitude |M| = Ms, but the magnetization can have different orientations. The applied magnetic field changes the domain orientation, and the resulting net magnetization is found from the following nonlinear implicit relation:
The effective field in the material is given by
where the matrix α characterizes the interdomain coupling.
The magnetization shape is characterized by the function L with the following properties:
For weak effective fields, the magnetization is nearly linear
and can be characterized by the initial magnetic susceptibility matrix χ0.
For strong fields, the magnetization magnitude approaches the saturation value
The magnetization shape is characterized be the Langevin function
where χ0 is the magnetic susceptibility in the initial linear region.
Other possible choices of the L function are a hyperbolic tangent, which is sometimes referred to as the Ising model
and a linear function
The latter option will make it possible to find an explicit expression for the magnetization. However, such model does not have a proper saturation behavior, and thus it should be used only in the operating range far from saturation. Both the Langevin function and hyperbolic tangent models requires the magnetization vector components to be treated as extra dependent variables.
Possible hysteresis of in the material magnetization is characterize using the Jiles–Atherton model. The model assumes that the total magnetization can be represented as a sum of hysteretic and anhysteretic parts, the latter one is given by
The change in the total magnetization caused by the change on the effective magnetic field is represented as
where cr is the reversibility parameter, and kp is the pining loss parameter. The above can be solved using either a time-dependent analysis or a stationary parametric sweep.
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.
The options Effective medium and Archie’s law require additional subnodes. If Effective medium is selected, a Effective Medium subnode is available from the context menu (right-click the parent node) as well as from the Physics toolbar, Attributes menu. If Archie’s law is selected, add an Archie’s Law subnode in the same way. These subnodes contain additional settings to specify how the material properties are computed. Effective medium models a mixture of materials whose properties are computed by averaging the properties of the components. Archie’s law models a conductive liquid in a nonconductive matrix.
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. If Effective medium is selected, a Effective Medium subnode is available from the context menu (right-click the parent node) as well as from the Physics toolbar, Attributes menu, which can specify the relative permittivity of the mixture.