Example for anti-plane deformation in 2D?

I was looking around for a 2D anti-plane strain example, e.g. a vertical cross section through a strike-slip fault. The closest I’ve found is the 3D strike-slip benchmark (Strike-Slip Benchmark — PyLith 3.0.3 documentation), but is it possible to do something similar in a 2D cross section?

I think I would need to specify an out-of-plane displacement field via dirichlet boundary conditions along the edges and on the fault. E.g, I want to specify the z-component of slip on a 2D mesh that sits on the plane z=0. If this is possible, I’d be happy to contribute an example once I can get it working. Any advice is appreciated!

PyLith has never supported 2D anti-plane strain. We recognize this can be useful but it requires FE infrastructure to do special 2D integrations in 3D space. This could be something worth discussing as we have more FE infrastructure in place than we have in the past to deal with surface integration in 3D, which is similar.

I think the only workaround is to make a 3D problem that is 1 cell thick in the anti-plane direction. You would need to be careful about what is happening in the out-of-plane direction to ensure consistency with a 2D anti-plane implementation.

Understood, while I think it would be great to get a true 2D implementation of antiplane strain working, I can certainly see the difficulties.

Creating a 1-cell-thick 3D model and constraining the in-plane displacements along those boundaries to be zero sounds like it could work, but maybe there are subtleties I’m not seeing. I’ll give it a try!