shear flow - periodic boundary

Asked by Chiara Modenese on 2011-11-03

Hi,

is it possible to apply a velocity gradient along the vertical direction only but at the same time without rotating the periodic cell? To say it better: imagine the lateral periodic boundary remains vertical while you apply a velocity gradient along the vertical direction.

Thanks for hints,
Chiara

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Last query:
2011-11-07
Last reply:
2011-11-07

Do you mean imposing velGrad(x,y) while keeping a quadrilateral shape for the period? No, it is not possible.

On 3 November 2011 16:20, Chareyre <email address hidden>wrote:

> Your question #177419 on Yade changed:
> https://answers.launchpad.net/yade/+question/177419
>
> Status: Open => Answered
>
> Chareyre proposed the following answer:
> Do you mean imposing velGrad(x,y) while keeping a quadrilateral shape
> for the period? No, it is not possible.
>
Yes, I meant that. It is not possible because of the way the periodic works
in Yade or it is not possible in general? I have seen a few papers where
they shear the material using a periodic cell but there is no rotation of
the cell itself (the lateral imaginary boundary remains vertical, say).
However a gradient is applied to the particles. Periodicity in space and
velocity gradient cannot be distinguished?

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It is impossible in general. If you have a periodic patern like this:

     ____
   / / /
  ____
/ / /

... and if you look at it through a rectangular window, then what you see in the rectangle is not a periodic (by translating the rectangle vertically, you see something different).

It is of course always possible to draw spheres in a rectangle, but it doesn't show the real period. Maybe the papers you mention did that.

Apparently there is another method used in fluid mechanics called Lees
Edwards where the periodic cells are sheared one over the other but there
is no rotation of the period itself. Apparently this is a good method for
large strains.
ref: The computer study of transport processes under extreme conditions by
Lees and Edwards
It is rather short paper, interesting the way the apply the shear with
periodic boundary...

On 7 November 2011 08:41, Chareyre <email address hidden>wrote:

> Question #177419 on Yade changed:
> https://answers.launchpad.net/yade/+question/177419
>
> Status: Open => Answered
>
> Chareyre proposed the following answer:
> It is impossible in general. If you have a periodic patern like this:
>
> ____
> / / /
> ____
> / / /
>
> ... and if you look at it through a rectangular window, then what you
> see in the rectangle is not a periodic (by translating the rectangle
> vertically, you see something different).
>
> It is of course always possible to draw spheres in a rectangle, but it
> doesn't show the real period. Maybe the papers you mention did that.
>
> --
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Thanks for the paper!
Fig. 1 is an example of what I said: a simple rectangle arrangement can't describe a sheared media. They have to use the trick of shifting horizontaly the rectangles of the upper/lower layers, ok why not, but then it implies complex rules for moving the particles from one period to the other (see equations 1 to 4 + associated comments on the P, P', P'' problem, and also the velocity shift problem).

It terms of implementation it is horrible. You have to track each particle to detect when it leaves a period and enter another, because you must apply an instantaneous position jump to it. In yade, we don't do anything special when the particle leaves a period. The other problem is that a particle can have neighbors that are far away in the y direction as soon as the neighbors are in different periods, it means the AABB bounding cannot be employed.

You refer to large strains as if it was a problem, why? There is no limitation of the current algorithms we have, and there are no specific problems with large strains in DEM in general.

On 7 November 2011 11:15, Chareyre <email address hidden>wrote:

> Your question #177419 on Yade changed:
> https://answers.launchpad.net/yade/+question/177419
>
> Status: Open => Answered
>
> Chareyre proposed the following answer:
> Thanks for the paper!
> Fig. 1 is an example of what I said: a simple rectangle arrangement can't
> describe a sheared media. They have to use the trick of shifting
> horizontaly the rectangles of the upper/lower layers, ok why not, but then
> it implies complex rules for moving the particles from one period to the
> other (see equations 1 to 4 + associated comments on the P, P', P''
> problem, and also the velocity shift problem).
>
> It terms of implementation it is horrible. You have to track each
> particle to detect when it leaves a period and enter another, because
> you must apply an instantaneous position jump to it. In yade, we don't
> do anything special when the particle leaves a period. The other problem
> is that a particle can have neighbors that are far away in the y
> direction as soon as the neighbors are in different periods, it means
> the AABB bounding cannot be employed.
>
I agree with you. I simply wanted some help to understand the difference
between what we are doing with respect to many others and so understand
their results (you will find plenty of papers in FM which refer to this
sort of implementation). At the beginning I thought we might not deal
correctly with large strains but I understand is not true in Yade at least
(we do not actually define a strain tensor and so on as we were saying).

Thanks for comments on the matter so far,
Chiara

> You refer to large strains as if it was a problem, why? There is no
> limitation of the current algorithms we have, and there are no specific
> problems with large strains in DEM in general.
>
> --
> If this answers your question, please go to the following page to let us
> know that it is solved:
> https://answers.launchpad.net/yade/+question/177419/+confirm?answer_id=4
>
> If you still need help, you can reply to this email or go to the
> following page to enter your feedback:
> https://answers.launchpad.net/yade/+question/177419
>
> You received this question notification because you asked the question.
>

You're welcome. :)

I believe our PBCs are mathematically equivalent to the ones found in FM (including the paper you mentionned) or in Radjai. They only differ in some implementation details (reduced coordinates in Radjai, shifted rectangles in the reference above, and probably many other variants).
It is also possible probably to find examples of periodicity implementations not accounting for the macroscopic velGrad (especially in the field of quasistatic regimes where it doesn't really matter), since it is easier to implement.

I don't see any of these implementations having specific problems with large strains as soon as the model is using a step-wise eulerian formulation. Large strain could only be a problem if the evolution at time t was a function of positions at time 0 (lagrangian formulation). I don't know any example of this kind in DEM-like methods.

Can you help with this problem?

Provide an answer of your own, or ask Chiara Modenese for more information if necessary.

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