# Magnetic materials with nonlinear characteristic

## Reminder of the problem

In a Steady state AC Magnetic application, the unknown variables (potentials) and the physical quantities which derive from them (magnetic field strength and magnetic flux density) are sinusoidally time-varying.

Thus, the representation by complex images is used, and the solution is obtained with only one solving.

Hence, it is not possible to take into account magnetic materials with nonlinear
characteristics. In fact, in the presence of nonlinear materials, the magnetic field
strength **H** and the magnetic flux density **B** cannot vary simultaneously
sinusoidally (see § Equivalent models for Steady state AC Magnetic
applications).

## Energetic method (equivalence)

To take into account material with nonlinear characteristics of magnetization, a method
based on energetic equivalence allows defining a relation **B(H)** called
“equivalent”, which considers that the equivalent **H** and **B** quantities are
sinusoidally time-varying.

This method as well as the models proposed in Flux are presented in chapter Materials: principles (see § Equivalent models for Steady State AC Magnetic applications).

## Warning

This method provides good results for global quantities. The computation of local quantities is available, but the results can be meaningless.