yade-users team mailing list archive

[Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx>]

> Is this explanation at least a little understandable and useful? :-)
>
>   
It is an interesting explanation, I didn't put it exactly that way 
before, but I buy this.

My simplest explanation is actually in the documentation of the class, 
let me know if it is not clear enough :

/"The compliance of one sphere under symetric point loads is defined 
here as 1/(E.D), with E the stiffness of the sphere and D its diameter, 
and corresponds to a compliance 1/(2.E.D) from each contact point. The 
compliance of the contact itself will be the sum of compliances from 
each sphere, i.e. 1/(2.E.D1)+1/(2.E.D1) in the general case, or 1/(E.D) 
in the special case of equal sizes. Note that summing compliances 
corresponds to an harmonic average of stiffnesss, which is how kn is 
actually computed in the :yref:`Ip2_FrictMat_FrictMat_FrictPhys` functor."
/
Actually, Nasibeh, we are really computing springs in series in Yade, 
and k=ka*kb/(ka+kb).
But here ka=2.Ea.da and kb=2.Eb.db, which gives the factor 2 in k.
In one sense, it is like putting two rods of length L1/L2 in series and 
defining the stiffness of the "contact" between the rods looking at the 
window L1/2 < x < L1+L2/2.

Bruno


> an example: let's have two springs (rods) made of steel with Young's modulus Ea=10. the rod stiffness of each spring is kLa = EaA / La = 10*2/5 = 4. If You put them into a serie and apply force F, the extension of such system would be twice as big as the extension of one spring. The rod stifness of the system is halved: kL = kLa/2 = 2. On the other hand, the value of the material stiffness E remains the same, E... You can try to apply aforementioned formulas :-)
>
> In Yade, (I suppose :-) the stiffness is considered as the material stiffness, and therefore the value of the contact stiffness is computed using harmonic mean..
>
> Best wishes
>
> Honza
>
> ______________________________________________________________
>   
> > Od: "Nasibeh Moradi" <nasibeh.moradi@xxxxxxxxx>
> > Komu: yade-users@xxxxxxxxxxxxxxxxxxx
> > Datum: 19.04.2010 10:54
> > Předmět: [Yade-users] harmonic average of stiffness
> >
> > hi,
> >
> > in contact law, harmonic average is used  for computing kn and ks in contact
> > between 2 body, why harmonic average?
> > in some papers, the springs are in serie, then k=ka*kb/(ka+kb),
> > but in harmonic average k=2*ka*kb/(ka+kb)
> >
> > Nasibeh Moradi
> >
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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
________________