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Here is the LS-Dyna example for the documentation. I implemented a standard Neo-Hookean material last week anyway to check some interfaces, so I chose this for the documentation example. The elastoplastic code got a bit involved with regard to the tangent (due to the LS-Dyna umat-utan split), so I guess the minimal Neo-Hookean is more appropriate at first. The picture will probably not be loaded (no clue how to set proper paths), so you can also view it here: example_neohooke-LSDYNA. Hopefully, the remaining formatting is okay (I'm used to Doxygen).
Herein, I also tested the approach to use different modules. To avoid mixing things up, further information is collected in a following pull request as a basis for our ongoing discussion.
I hope, I got the pull request right. Just reject it and let me redo it, in case something is fubar.