yade-dev team mailing list archive

[chiara modenese <c.modenese@xxxxxxxxx>]

2010/4/3 Václav Šmilauer <eudoxos@xxxxxxxx>

> Hi folks (Bruno),
>
> where exactly does come the damping formulation we use in Yade? I
> thought it was Cundall's damping (I don't have fulltexts of his papers,
> sorry), but Hentz in his thesis reports formula from Cundall's book
> "Analytical and Computational Methods in Engineering Rock Mechanics",
> which is supposedly like this (3.21, pg. 71):
>
>  Δa=-λ|a|(v/|v|)          (*)
>
> (a=acceleration, v=velocity, λ=damping coeff. I write a=F/m instead of F
> as he does)
>
> In Yade, we damp per-component,
>
>  Δaᵢ=-λaᵢsgn(Fᵢvᵢ'),   (**)
>
> where vᵢ'=(vᵢ+½(aᵢΔt)), approximate of velocity between this and next
> timestep.
>
> I understand that in (*) you have to compute 1 square root, have to make
> sure that |v|>0 etc, making (**) more efficient, but also less obvious
> (it is not invariant to coordinate system rotation, for instance :-|)
>
> In short, can I get some references for what we use?
>

A reference for this global damping can be found in PFC3d manual (chapter
Theory and background) where they propose:

Fdi=-λ|Fi|sgn(vi)      (***)

so basically the same as in Yade (**). The two formulations act exactly in
the same manner (they oppose the motion), I suppose that is just a matter of
efficiency to choose the (**) equivalent to (***).

Chiara

>
> Cheers, Vaclav
>
>
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