A common assumption in modeling is that a material responds linearly with respect to an applied stimulus as long as that stimulus is not too large. For example, Ohm’s law stipulates a linear relation between electric field strength and current density in a conducting medium;

\mathbf{J} = \sigma \mathbf{E}

a relation that, for many materials, is surprisingly accurate over a wide range of electric field strength.

In this respect, ferromagnetic materials are fundamentally different as the level of magnetization depends nonlinearly on the magnetizing field, even for small values. There is also a dependency on the magnetization history (*hysteresis*) that is demanding and difficult to include in simulations. An example of a steady-state hysteresis loop is shown below.

Trying to capture this in a material model for design and simulation is possible, but generally leads to very long simulation times. Another major challenge is that the parameters of a hysteresis model are not directly measurable but have to be found through elaborate curve fitting methods. For most design purposes, only the average B-H curve, which incorporates magnetic saturation effects, but not hysteresis, is needed:

Measuring B-H curves involves expensive equipment and requires considerable skill and experience, and published B-H curves are most often provided only graphically. When digitizing such curves, it is important to acquire enough data pairs and to avoid introducing too much digitizing noise.

Seen from the modeling and simulation perspective, for numerical efficiency and stability a B-H curve should be smooth, without local maxima or minima, and extrapolate correctly as in the saturation limit the slope of the B-H curve should approach the permeability of free space.

Thus, the new nonlinear magnetic materials database contains B-H curves that are densely and accurately sampled, have the hysteresis effects averaged out, and extrapolate correctly in the saturation limit.

The nonlinear magnetic materials are available in a dedicated section in the “Add Material” dialog in the COMSOL user interface. Here we use it for the soft magnetic core in a model of a generator with permanent magnets in the rotor. Bringing up the Add Material window, there is a Nonlinear Magnetic section available.

Once added to a model, the B-H curve is accessible for plotting (first quadrant):

and for use in the model:

Depending on the magnetic formulation used in the model, either the B-H curve or, as here, its inverse, the H-B curve is used. Both are provided by the nonlinear magnetic library materials together with electrical permittivity and conductivity.

Altogether there are 165 materials falling into the following categories: Silicon Steels, Non-Grain Oriented; Silicon Steels, Grain Oriented; Metglas, Nano; Cobalt Steels; Nickel Steels; Stainless Steels; Low Carbon Steels; Castings; Powder Iron Core; Alloy Powder Core (including Ferrites). These are virtually available at your fingertips with the AC/DC Module and COMSOL Multiphysics version 4.4.

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