You need multiple string winding. At 111K skin depth is ~ 4.5E-4 cm. Although datasheet does not indicate any details on winding, and current rating are DC only so it is likely that it is build with single strand, which won't work for rated current at 111K Hz.
What are your actual requirements for AC losses? I can pretty much guarantee an off the shelf inductor exists, but it might be bigger and more expensive than you wish. But maybe still cheaper than rolling your own solution, especially if you try to use litz wire.
But yeah you'll need the DC rating to be much higher than your expected RMS/average current, since DC ratings don't take core losses or skin effect into account.
Definetely wrong. You get about 0.2 mm for Cu. So the windings resistance will be increased, but not extreme.
In my opinion, you should use an inductor designed as storage inductor for SMPS, preferably wound with flat wire. The said Bourns type hasn't clear specifications to know e.g. about the core losses at 110 kHz.
FvM is correct, for 111K, skin depth for cu would be 0.0198399 cm, which would be ~0.2mm. Seems that I punched in some wrong number on calculator.
Sorry about this. Thanks FvM.