This post is intended to collect some ideas before starting: Has anyone already developed such a solver or knows a good starting point?

Have you taken a look at the deal.II Code Gallery?
  https://dealii.org/developer/doxygen/deal.II/CodeGallery.html
There are a couple more large-deformation codes.

There is also this article from Thomas Wick about a deal.II-based code for FSI:
  https://media.archnumsoft.org/10305/
I believe that the code that goes with the article is freely available as well.

Best
 W.

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Wolfgang Bangerth          email:                 bange...@colostate.edu
                           www: http://www.math.colostate.edu/~bangerth/

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