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For structural mechanics, such as linear elasticity, I am aware of BCs such as a prescribed displacement (Dirichlet) or a prescribed traction (Neumann).

Is it possible that a boundary can have a mixture of prescribed displacement and prescribed traction, i.e., a mixture of Dirichlet and Neumann BCs for the same boundary? It would seem that this would make the problem over-specified?

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  • $\begingroup$ Are you talking about mixed boundary conditions, like Robin? en.wikipedia.org/wiki/Robin_boundary_condition $\endgroup$ – Anton Menshov♦ Apr 27 '18 at 17:45
  • $\begingroup$ @AntonMenshov Yes, I think so. If not, then at least it is analogous to that. I am trying to picture how this would even work in structures, and I cannot think of how it would. $\endgroup$ – user27504 Apr 27 '18 at 18:30
  • $\begingroup$ One thing is having Robin boundary conditions (a linear combination of displacements and tractions) and another one is to have both displacement and tractions prescribed over a region. Which case are you interested in? $\endgroup$ – nicoguaro♦ Apr 27 '18 at 18:46
  • $\begingroup$ Could you give an example of each? I guess I am not seeing how the two can be applied to the same boundary. $\endgroup$ – user27504 Apr 27 '18 at 19:58
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    $\begingroup$ The mixed (Robin) condition states that there is a linear relationship between the traction and the displacement, i.e. some kind of spring-type boundary condition. $\endgroup$ – knl Apr 27 '18 at 20:43
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You can't prescribe both Dirichlet and Neumann conditions, but you can prescribe a Robin-type boundary condition in which the normal stress (traction) is proportional to the displacement. You can think of this as a case where each point at the boundary is tethered by a little spring to its undeformed location, with the springs producing a force that is proportional to the displacement from the undeformed configuration. An example of how this could be done is when your body is in contact with another body.

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