What are the symmetry conditions for a 2D deformation diffusion problem with symmetry surface y = 0?

I am thinking of the following:

no displacement on symmetry surface: u_y = 0 at y=0

no flux through symmetry surface: j_y = 0 at y=0

Do I also have to enforce 0-slope at symmetry surface? Such as

du_y/dy = 0 at y=0

Which BCs are needed?

The additional BCs needed for the solid subproblem are that the x and z components of traction on the boundary are zero. You are probably already enforcing these weakly if you are using the typical weak form of elasticity and not assembling any boundary term at y=0.

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Great, yes, I am using the typical weak form, so that is taken care of. Just a last check, so du_y/dy = 0 at y=0 is not needed at all? Many thanks!

No, constraining the normal displacement and weakly enforcing zero tangential traction should be sufficient.

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Alright, got it, thank you!