Hi Chiara,
I didn't take time to reply as it would need a long discussion. Keep
looking into MD litterature and you should find questions to your
answers, be it in a formalism that is excessively complex.
I don't agree with your equations below (giving Cundall way). I don't
think anybody ever wrote equation (1). There is a very BIG difference
between vel=... and vel+=...; Cundall is using vel=... where vel is the
mean field velocity.
Envisage a periodic cloud deforming at constant strain rate, without
contact between particles, and see what will happen if you write
vel+=something at each step.
________________________
Cundall way (as you rightly pointed out) is the following:
*** update of velocities (he does not, but as you already said
this would be the solution):
vel+=velGrad*vel*dt (1)
*** update of positions:
pos+=(velGrad*vel*dt)*dt
________________________
Currently in Yade (NewtonIntegrator):
*** update of velocities:
vel+=(velGrad-prevVelGrad)*pos
*** update of positions:
pos+=(velGrad-prevVelGrad)*pos*dt
________________________
There is a term of difference between these two formulations.
Basically, it is like writing:
pos_Yade = pos_Cundall - prevVelGrad*pos*dt
That said, why would you use (velGrad-prevVelGrad) instead of velGrad?
Which is the unit of measure of the rate of the gradient of velocity?
Is this formulation consistent? Taking the rate of velGrad instead of
velGrad is not really the same.
The acceleration of bodies (vel+=...) is linked with the acceleration of
the period (gradVel-prevGradVel). It is consistent.
One more question. Why do not we move the spheres through the periodic
boundaries instead of updating their positions? Would this be
possible? I mean, like treating the periodic boundaries as walls. ATM,
we use the rule of continuum mechanics to updated positions of
discrete particles, but is this correct dealing with a particulate
system? Would not be better to apply the strain rate to the moving
periodic boundaries and as a consequence moving the balls?
I don't understand, sorry. Periodic problems don't have boundaries at
all. So, what is the strain rate of boundaries?
Bruno
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