yade-users team mailing list archive

[Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx>]

chiara modenese a écrit :
> On 2 June 2010 17:06, Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx 
> <mailto:bruno.chareyre@xxxxxxxxxxx>> wrote:
>
>     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.
>
>
> What do you mean as mean field velocity ?
> To report exactly from his paper what he wrote in terms of 
> displacement increment :
>
> delta_u = delta_u(real_vel) + gradVel*pos*dt; (1)
>
> where :
> delta_u(real_vel) = vel*dt; (vel is from the real particle velocity, 
> hence = a*dt)
>
> So the increment of velocity I guess would be given by :
>
> delta_v = vel + gradVel*pos; (2)
>  
Heh, no! If you derive (1) vs. time, it will not give (2).
First, divide (1) by dt to get instantaneous quantities :

du/dt = vel = du_real/dt + gradVel*pos = v_real + gradvel*pos
(v_real is not "real" at all, it is the velocity in the local 
coordinates of the corresponding cell, the real one is the sum)

The time derivative gives :

acceleration = acceleration_real + d(gradVel)/dt*pos + gradVel*d(pos)/dt

first term : comming from contact forces
second term : (grad-prevGrad)*pos (after integration on dt)
third term : convective term.

The third term blocks elastic waves. That is why I'm not sure which one 
is best. HCresize=1 (only first two terms) will gives periodic waves, 
HCresize=2 will stop them (I could confirm in simple 1D cases). For slow 
deformation, the convective term is negligeable and both gives the same.

Cheers.

Bruno









> That is why I was writing in my previous post :
>
> vel+=vel+gradVel*pos; (I was only missing the vel given by a*dt, but I 
> thought it was implicit)
>
> Is this wrong ?
> IICR, you were writing the same thing in a previous post in this 
> thread, like:
> if (homotheticCellResize>1) 
> state->vel+=scene->cell->velGrad*state->vel*dt;
>
> and now you say that equation
> vel+=velGrad*vel*dt   (1)
> is wrong. Does not look exactly the same you wrote ?
>
> 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
Fax : 33 4 76 82 70 43
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