Is there any way I can simulate the expansion joint so that it can cycle between compression and extension? I will be adding mating flanges on both ends and fixing one end while the other flange will compress the joint and extend the joint due to thermal expansion and contraction. This is very similar to a spring or coil adaptive simulation.
As far as I am aware Inventor cannot simulate any displacements due to thermal loading. Nevertheless if you know these displacements you might be able through variable dimensions in "Inventor studio" to visualize the expansion & contraction of the joint. (is that what are you looking for?)
I am not sure if you ever had the chance to simulate thermal stresses but I can tell you that is not something very difficult. Below is a link of thermal stress analysis with autodesk simulation. In fact you can find countless tutorials online that can assist you to model your own simulation as it seems to be in a quite normal level of difficulty.
So, in case that you are looking to find the actual displacement (of contraction or expansion) and not just to visualize the movement of a rubbery joint you will need something more than a CAD software...
The question is....
"Random visualization or a Relative accurate approximation of displacements"
Let me know what you are looking for and in what F.E.A. software you have access.