I'm trying to teach myself FEM. The problem I have in mind is to completely investigate a plastic (e.g rubber band) being stretched (therefore, boundary conditions move as you stretch). I imagine this is a very simple problem but I can't find it covered in common FEA books. Does anybody know a good source and software I can play around with?
Modelling the stretching of objects made of rubber-like material is quite a complex task: you need to take into account hyperelastic constitutive equations, large strains, and write momentum conservation equations in the current configuration and not in the reference one (large displacements).
This results in a highly non-linear problem that can be solved (if mesh distortion does not becomes to large) by a purely lagrangian approach in FEM. (If mesh distortion becomes a problem, remeshing techniques or ALE approaches are to be considered.) In a Lagrangian approach you do not have "moving boundaries", since Dirichlet conditions are still expressed as displacements with respect to the reference configuration. (Of course if you remesh or switch to an ALE formulation, tracking moving boundaries is a problem to deal with.)
This said I think that this problem is not well suited to learn basic FEM. Linear problems (like heat conduction under some simplifying assumptions or small strain/small displacement linear elastic solid mechanics) are more useful.