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Consider a thermo-mechanical coupled problem, where coupling exists from both the sides, mechanical loading producing thermal effects and vice versa. In such a case, is it necessary to always prescribe a thermal boundary condition along with a mechanical boundary condition on the same boundary for the problem to give valid results?

For example, when prescribing mechanical load with temperature or prescribing heat flux with displacement.

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    $\begingroup$ Boundary conditions are specific to individual equations. Care to share the model you're considering in formulas? $\endgroup$ – Wolfgang Bangerth Nov 21 '15 at 1:46
  • $\begingroup$ I agree with @WolfgangBangerth, the BCs you apply should match whatever physical situation you're trying to model. Often BCs for different physics will be applied at the same location, but this is not always the case. Consider internal fluid flow in a pipe with heat transfer. BCs for the fluid are likely applied on the interior of the pipe while BCs for heat transfer are likely applied on the exterior of the pipe. $\endgroup$ – Charles Apr 26 '16 at 1:43
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It is very much problem dependent, but the fact that it is coupled doesn't matter.

In other words, if you have BC's properly defined for the thermal model, ignoring the mechanical aspects, and if you have BC's properly defined for the mechanical model, ignoring the thermal aspects, you have BC's properly defined for the coupled system. It's not a bad idea to take a "divide-and-conquer" approach to coupled problems, setting up and solving each problem individually, then doing a one-way coupling, then doing the full coupling.

In general, there's a few heuristics to keep in mind when solving such problems:

  • For each submodel, in each dimension, you need the same number of BC's as the highest order derivative in the problem. For the heat equation, this is typically 2nd order in space, and thus you need two BC's specified
  • What type of BC you use (Dirichlet, Neumann, Robin) and where you apply it depends on what you are modeling -- remember, you can apply BC's at $\infty$
  • For the heat equation, and others, you can't have Neumann type BC's on every boundary in a steady state problem without add'l information. You need to specify the temperature somewhere or sometime (Note: this isn't necessary a hard-and-fast rule for all models you will encounter, but if it comes up, take a second look)
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It depends on what you understand on valid results. I would say that if for instance you want to determine how much of your strain energy dissipates to heat it would be sufficient to use periodic boundary conditions for the strain on a defined hull of your representative volume element and embed your element into a matrix so that the produced heat is transferred to the matrix.

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