# Re: [deal.II] Parasitic stress in corners with periodic boundary conditions

```Hi, sorry for this late reply. I missed it and realized just now. I found
the problem, which is simply that if the whole system is fully periodic ( I
mean, for example from plane to torus topology) then the 4 corners become
effectively fixed (the other possibility would be rigid body motion). The
fact that this 4 nodes become fixed, makes that when some eigenstrain is
prescribed somewhere, unexpected stress appears close to the corners as the
system can't fully relax there. I think this is something one was to live
with. I didn't see it with other FEM packages because the solution suffered
some post processing before I got it, which smoothed the result and somehow
hide this.```
```

On Monday, 2 June 2014 00:59:11 UTC+2, Wolfgang Bangerth wrote:
>
> On 05/28/2014 10:29 AM, David F wrote:
> > Hello, my problem is the following:
> >
> > I prescribe an eigenstrain value in one element of the grid (i.e., an
> inner
> > element undergoes a certain transformation and this introduces strain
> and
> > stress in the rest of the grid), and everything works fine for normal
> > boundaries and periodic boundaries. However, if one pays close
> attention, for
> > the periodic boundary solution in the corners of the grid one can see
> some
> > parasitic stress that shouldn't be there.
> >
> > I think the reason is the following: prescribing, let's say, a shear
> > eigenstrain in one element, the four corners (in 2D) of the grid deform
> in
> > opositte directions if the boundary is not periodic, therefore when it
> is
> > periodic the four corners are in fact "the same", and these 4 opposite
> > displacements would add up to 0, effectively fixing the "corner node".
> This
> > seems to me a natural problem of FEM and periodicity, so I have no clue
> how to
> > correct this with code.
> >
> > I have used other FEM packages for solving exactly the same problem I
> > described, and somehow this is not happening, so there must be a way to
> avoid
> > this. I am not sure if it has to do with my implementation of the
> periodic
> > boundaries, or maybe the way in which deal.ii deals with periodicity is
> the
> > reason, or maybe I have to apply some kind of postprocessing correction
> of
> > which I am not aware yet.
> >
> > Does anyone know why could this be?
>
> I don't know myself. Maybe someone else does. But I'd like to point out
> that
> using periodic boundary conditions is equivalent to looking at a problem
> where
> you have periodic array of sources. Is the element where you prescribe the
> eigenstrain by chance close to a corner of your domain? If so, I would
> expect
> there to be some strain close to the opposite corner as well, simply
> because
> there is a source (outside your domain) close to that opposite corner.
>
> It may be worthwhile sending a picture that shows what you are observing.
>
>
> > P.S.: my periodic boundary implementation is a direct extension of
> step-45 and
> > everything but these small parasitic stress in the corners is pretty
> accurate,
> > so probably a problem in the code is not reason. Should I try with
> > DoFTools::make_periodicity_constraints or do you the problem will be
> exactly
> > the same?
>
> Hard to tell. It's probably worth a try.
>
> Best
>   W.
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth               email:            bang...@math.tamu.edu
> <javascript:>
>                                  www: http://www.math.tamu.edu/~bangerth/
>
>

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