[DonRotolo]

This is not fabric. Think "soft stone" for an approximation. As stated, thick materials (it comes up to 3/4") are counterbored and riveted, thin material is glued. 3M 77 is a good start, or some epoxy resin perhaps. If you expect any kind of heat, get a glue that can handle it.

If anyone works on cars, they might be able to show you a car's brake pad, which is a lot like this stuff.