Simulation of distortion from output inductor in class D amplifier, e.g. inductor non-linearities modelling
Polarization is just a matter of sign, while the hysteresis window is inherent to magnetic cores. What distorts the current is the B-H curve getting into the nonlinear region. Well, technically, it's not linear even in the &quot;linear&quot; region, but it has good linearity there. For ferrites (which you'll probably use), the B-H curves will be square-ish, so the linearity is even better. When you get into the saturation region, the core saturates, the permeability drops, so the inductance drops, causing the current to rise. The effect is a pointy current waveform, seen in L1 below (nonlinear core) vs L2 (equivalent linear inductance):

If it's easier, think of the current mapped from a linear region to a tanh(), so the current will tend to be an atanh(). For small variations of B, H will rise exponentially.
The above is a Chan core, built-in in LTspice, but if you're looking for more accurate waveforms, you should look into the Jiles-Atherton model. If you integrate the voltage across the inductor and plot it agains the current through it, you'll see the B-H curve. For some differences between cores, see this.