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I have been looking at hoop stresses and the information I have found hasn't been all that useful to me as I am having a hard time converting the thermal contraction of a system into a pressure for the equation (stress=a+b/r^2). This is the thick walled hoop equation

The disc is a few microns of copper on 0.7mm silica and from the thermal contraction the disc bends from Stoney's equation. The discs are solid (no hole) and have a radius of 40mm.

as the disc is solid b=0 so we only have a which is apparently the pressure. As all of the stresses are coming from thermal contraction I'm not sure if it will all cancel out.

the radius of the copper contracts by 0.1304mm and the silica contract by 0.0032mm if its required.

Thanks for your time