Hi David,
Great to hear that, I am a fan of open-source software development in our field and appreciate the work of the preCICE project!
The tutorial steps you might want to look at are 8,18,24,44,46 & 62; the code gallery also offers quite some interesting codes, among which
and
might be of most relevance to you.
The code by T. Wick is available here
You might simplify one of the codes from the code gallery and plug in the element integration routine from the last code to get to 'geometrically nonlinear elasticity'.
I have done some similar things, thus have a bit of code in that direction. If you are interested in working together, just mail me.
Good luck & Kind regards,
Richard