There are currently Unbreakable Materials that can only be destroyed by making physics take effect and pushing them out of the world or blowing them up with Trigger Bombs. The names of the materials have not yet been released to the public.
Yet there are also unbreakable Materials, even with bombs and most of the times you cannot even force them to be pushed around. These are Black Onyx like looking rocks. One of them is right at the Spawn when you go out of the Start Pyramid and look to your right.