We try to simulate a metal forming process in deal.II, which also requires 
modelling contact between deformable solid bodies (possibly reducible to 
one deformable body and rigid tools). Developing a capable and somewhat 
robust contact formulation itself is challenging. Therefore, I would like 
to ask whether there is already experience, insights, or existing contact 
implementations available in deal.II that could be used or adapted.

I am aware of the following contact related implementations:

   - deal.II step 41 (
   https://www.dealii.org/current/doxygen/deal.II/step_41.html) and 42 (
   https://www.dealii.org/current/doxygen/deal.II/step_42.html, 
   
https://wwwold.mathematik.tu-dortmund.de/papers/FrohneHeisterBangerth2014.pdf), 
   which deal with contact. However, these formulations seem quite specialised 
   and appear to be not easily extendable to the problem at hand (involving 
   friction, large sliding, closing/reopening of contact surfaces, etc.), 
   right?
   - Further, I came across Maien Hamed's (@maieneuro 
   <https://github.com/maieneuro>) work on an ALE approach including 
   contact (2022/2023: http://hdl.handle.net/11427/36777, 
   https://doi.org/10.1007/s00466-023-02303-0). His contact formulation 
   uses an augmented Lagrangian approach including friction and multi-body 
   contact, appears very capable and seems to be one of the most advanced 
   deal.II contact implementations so far. He was also active in the deal.II 
   Google group and on GitHub. Unfortunately, I cannot get a hold of Maien to 
   discuss the formulation and implementation. Maybe he receives a 
   notification about this topic or if anyone is in contact with Maien, I 
   would be delighted if they could make the connection. (my e-mail: 
   johannes.friedl...@fau.de)
   - Discussion on penalty method and convergence failure: (
   https://groups.google.com/g/dealii/c/uP8NgR0NKBc/m/t_asBiWvBwAJ)
   - "Modelling and numerical simulation of contact and lubrication" (
   https://nbn-resolving.org/urn:nbn:de:hbz:467-6816): Signorini- and 
   z-contact
   - "Cn continuous modelling of smooth contact surfaces using NURBS and 
   application to 2D problems" (https://doi.org/10.1002/nme.776)
   - "Goal-oriented mesh adaptivity in elastoplasticity problems" code 
   gallery program (
   
https://www.dealii.org/current/doxygen/deal.II/code_gallery_goal_oriented_elastoplasticity.html):
 
   Here a reference is made to step 41 and the nonlinearity due to contact is 
   mentioned, but I cannot find a contact implementation or usage.
   - "A barrier method for frictional contact on embedded interfaces" (
   https://doi.org/10.1016/j.cma.2022.114820): Uses XFEM to mimic contact.
   - "A phase-field method for modeling cracks with frictional contact" (
   https://doi.org/10.1002/nme.6242): Using a phase-field model to mimic 
   frictional contact in deal.II.
   - "Modelling and Simulation of Fluid-Structure Interactions with Contact 
   and Multiple Scales in Time" (
   https://www.math.uni-konstanz.de/~frei/Habilitationsschrift.pdf): FSI 
   with contact in deal.II

On the other hand, for instance MOEFEM (
http://mofem.eng.gla.ac.uk/mofem/html/) made great progress on contact 
approaches (e.g. including mortar contact). But I am not sure how much can 
be learned or taken from there into the deal.II world.

Contact seems to be a rarity in deal.II. But from the works above, I 
conclude that it is definitely possible in deal.II, it is just a hell of a 
lot of work. Further, my research focus is not on contact. So, being able 
to expand on existing works would be crucial and highly appreciated.

I certainly missed works on contact in deal.II above. Please feel free to 
extend and correct the above list of deal.II contact implementations to 
provide a summary and overview for the future. A clean and updatable list 
is available on GitHub (deal.ii issue #17304, 
https://github.com/dealii/dealii/issues/17304), which I will extend/correct.

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