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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