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" <[email protected]>
Komu: [email protected]
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
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