Chiara,
If you have your noze in papers now, I'll let you think about the code
below (uncommited). The first line is what is in the code already.
Checking with paper and pen, I found that current equation is
equivalent to Cundall/Thornton expression only in the limit case of slow
deformations. Out of this limit, they can differ a little. I wouldn't
bet on which one is better, for now I can only tell they are slightly
different. What do you think (if you read on molecular dynamics, you
probably know more than me already)?
The interesting thing is we can still write something _exactly_
equivalent to Cundall equation by updating velocity, this is what is
done below. I'll give again the choice between two types of scaling
probably.
Cheers.
Bruno
/Vector3r
dVel((scene->cell->velGrad-prevVelGrad)*/*scene->cell->wrapShearedPt(*/state->pos/*)*/);
state->vel+=dVel;
//This is the convective term, appearing in the time derivation of
Cundall/Thornton expression (dx/dt=velGrad*pos ->
//d²x/dt²=dvelGrad/dt+velGrad*vel), negligible in many cases but not for
high speed large deformations (gaz, turbulent flow,...). Emulating
Cundall //in an option, I don't especially recommend it. I know
homothetic 1 and 2 expressions tend to identical values in the limit of
dense quasi-static //situations. They can give slitghly different
results in other cases, and I'm still not sure which one should be
considered better, if any.
if (homotheticCellResize>1) state->vel+=scene->cell->velGrad*state->vel*dt;
/
chiara modenese a écrit :
Hello Bruno,
I am a little bit confused about the periodic. In
NewtownIntegrator we update the velocities and _then_ we integrate
the positions. This is exactly the way of Cundall (I am checking
the equations right now) except that he chooses to update
positions and not velocities (defining a strain rate instead of a
gradient of velocity which we said is fine but not in the general
case). I understand that the reason why Cundall updates the
relative velocities at contact (btw, according to his paper this
is not meant to be only for the shear direction) before going for
the computation of contact forces is that he was not updating the
velocities at the level of the integration. So my guess is: why do
we need to update the relative velocities if that has already been
done in NewtonIntegrator? That would have made sense if updating
positions and not velocities. Bruno, you said there was a problem
using periodic ScGeom before the last changes. Where you testing
with homothetic=1? Because I think that case you would have needed
to update velocities (which is not a problem in Dem3dofGeom).
I have been looking at molecular dynamics (sorry for my lack of
knowledge in this field) and I see that "shift2" as well as the
"shift" introduced recently by Bruno for the velocities, are
independent by the way we update displacements (or velocities) in
NewtonIntegrator. If I have got it right, this shift has to deal with
the periodicity (though I will reread carefully the part of the code
where this is computed). This shift is not described in Cundall paper,
that is why I got confused.
Btw, why do you choose to update the cell in Scene?
cheers.
Chiara
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Bruno Chareyre
Associate Professor
Grenoble INP
Lab. 3SR
BP 53 - 38041, Grenoble cedex 9 - France
Tél : 33 4 56 52 86 21
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