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?

  • $\begingroup$ 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
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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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    $\begingroup$ as another interpretation, you can have simultaneous traction and displacement in different vector orientations at a point or over a surface. $\endgroup$
    – george
    May 2 '18 at 16:45

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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