Is there any indication of what the Structural Integrity Field is actually made of?
The Structural Integrity Field is an application of EM Forcefield technology. The actual mechanics are technobabble (based on "projected energy") but broadly, it sits inside and around the ship's superstructure giving it extra strength, well beyond that which would be found in the materials used.
Per the Star Trek Encyclopedia;
A longer definition (and description of power usage) can be found below from the TNG : Technical Manual, along with the out-of-universe description why such a thing is needed;