I have a concrete expansion joing that failed. Looks to me like it was not the fiber type expansion joint, but some type of wood. Is there material I can fill the void, 3/4", with and it will expand and not rot.

3/4" is facirly large but there are rubberized liquid pour caulks made for this application. Caulking Compounds on ThomasNet.com (http://www.thomasnet.com/products/caulking-compounds-16820607-1.html)

You might want to place a caulking rod in the joint before caulking, like ballangerb1 says.