Linear magnetic behavior is defined by direct specification of magnetic permeability.

*MAGNETIC PERMEABILITY, TYPE=ISOTROPIC

*MAGNETIC PERMEABILITY, TYPE=ORTHOTROPIC

*MAGNETIC PERMEABILITY, TYPE=ANISOTROPIC

*MAGNETIC PERMEABILITY, FREQUENCY

Nonlinear magnetic behavior is characterized by magnetic permeability that depends on the strength of the magnetic field. The nonlinear magnetic material model in Abaqus is suitable for ideally soft magnetic materials without any hysteresis effects (see Figure 26.5.3–1) characterized by a monotonically increasing response in B–H space, where B and H refer to the strengths of the magnetic flux density vector and the magnetic field vector, respectively. Nonlinear magnetic behavior is defined through direct specification of one or more B–H curves that provide B as a function of H and, optionally, temperature and/or predefined field variables, in one or more directions. Nonlinear magnetic behavior can be isotropic, orthotropic, or transversely isotropic (which is a special case of the more general orthotropic behavior). More than one B–H curve is needed to define the nonlinear magnetic behavior if it is not isotropic.

Directional dependence of nonlinear magnetic behavior

Isotropic, orthotropic, or transversely isotropic nonlinear magnetic behavior can be defined. For non-isotropic nonlinear magnetic behavior a local orientation for the material directions must be specified (“Orientations,” Section 2.2.5).

Isotropic nonlinear magnetic behavior

For isotropic nonlinear magnetic response only one B–H curve is needed at each temperature and field variable value. Isotropic magnetic permeability is the default. Abaqus assumes that the nonlinear magnetic behavior is governed by

Input File Usage:	You define through a B–H curve:
	*MAGNETIC PERMEABILITY, NONLINEAR, TYPE=ISOTROPIC *NONLINEAR BH, DIR=direction The B–H curve in any direction (i.e., the nonlinear behavior in global direction 1, 2, or 3) will suffice as the nonlinear magnetic behavior is assumed to be the same in all directions.

Abaqus/CAE Usage:

Property module: material editor: Electrical/MagneticMagnetic Permeability: Toggle on Specify using nonlinear B-H curve: Type: Isotropic

Orthotropic nonlinear magnetic behavior

For orthotropic nonlinear magnetic response three B–H curves (one curve to define the behavior in each of the local directions 1, 2, and 3) are needed at each temperature and field variable value. Abaqus assumes that the nonlinear magnetic behavior in the local material directions is governed by

where refers to a diagonal matrix.

Transversely isotropic nonlinear magnetic behavior is a special case of orthotropic behavior, in which the behavior in any two directions is the same and is different from that in the third direction.

Input File Usage:	You define , , and , respectively, through three independent B–H curves, one in each of the directions 1, 2, and 3:
	*MAGNETIC PERMEABILITY, NONLINEAR, TYPE=ORTHOTROPIC *NONLINEAR BH, DIR=1 … *NONLINEAR BH, DIR=2 … *NONLINEAR BH, DIR=3 …

Abaqus/CAE Usage:

Property module: material editor: Electrical/MagneticMagnetic Permeability: Toggle on Specify using nonlinear B-H curve: Type: Orthotropic

Ferromagnetic materials can be magnetized by placing them in a magnetic field, which is typically created by applying currents in a system of coil windings surrounding the material being magnetized. These materials can be classified into soft and hard magnetic materials (see Figure 26.5.3–1). Soft magnetic materials lose their magnetization after removal of the applied currents (see “Nonlinear magnetic behavior”). Hard magnetic materials retain their magnetization permanently after removal of the applied currents. The leftover magnetization in a permanent magnet is called remanence, denoted by in Figure 26.5.3–2. This magnetization can be removed by applying currents in the opposite direction; the strength of the opposing magnetic fields that remove magnetization entirely is called coercivity, denoted by in Figure 26.5.3–2.

Permanent magnetization in Abaqus is suitable for hard magnetic materials when the magnets are operating around the point of remanence. This behavior captures the response of magnetization or demagnetization around the point of remanence, as shown by the darker descending line of the hysteresis loop in Figure 26.5.3–2. The underlying magnetic permeability can be linear or nonlinear. In either case, permanent magnetization is defined by its coercivity such that

*MAGNETIC PERMEABILITY
*PERMANENT MAGNETIZATION
direction of magnetization in the global system
magnitude of coercivity

*MAGNETIC PERMEABILITY, NONLINEAR
*NONLINEAR BH
input - by shifting the response to the right by 
*PERMANENT MAGNETIZATION
direction of magnetization in the global system
magnitude of coercivity