I think you should analyze the inner region, take the displacements from this and impose it upon the outer region in a separate model, superimpose the results in a third-party graphics...sorry, I can't keep going...WHAT are you talking about????
"A 2D Solid" is a misnomer...I assume you are referring to a plane stress or plane strain model. If that is the case, I would think you are probably modeling two rectangles the outer of which has a height that is the thickness of your plate and a width that is the perpendicular dimension of your plate. Then model the rectangle that would include the inner region of your plate.
Depending on what software you are using (see Greg's posting), you may need to duplicate your inner rectangle with properties of your outer rectangle (to close off the outer region). Not sure what mesher you are using. If an automatic mesher, you will need to do the duplicate rectangle that I mentioned.
Then follow rb's advice about assigning different material props.
After all this, I still have no idea if this even REMOTELY answers your question.