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Re: Periodic triaxial

 

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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