How to reproduce a smartphone cover material with some specific reflection patterns I am working on a smartphone render, on Blender 2.79 with Cycles, using mainly the new Principled shader. Everything is working perfectly, I am not new to 3D nor Blender, but there's a very specific surface that has proven difficult. 

The back cover of the phone is made of some sort of glass (tempered glass) on top of a plastic surface (as I have come to guess, I might be wrong); and the mix gives a very particular kind of reflections. 



I have managed to get close by combining Anisotropy and Clearcoat, but the result is still not satisfying. I'm even thinking about working without the Anisotropic reflections at all.

Here's a link to some pics of the real phone and some screens of what I have done so far.




I hope someone can help me with this.

Thank you
This is really just a supplement to Nicola's answer: my approach was to control the Anisotropic Rotation with a grad something like this:

simple

And a simple, dark, slightly blue-tinted glossy material, (roughness around 0.1).

resulting in this kind of response to peak light-sources in an HDR environment.



These are the nodes: I'm not knowledgeable enough in this area to justify them -  I've a feeling changing Anisotropic Rotation is equivalent to  rotating tangent space, bar some mapping, but how it's done in the Principled shader is something I have to look up.