Hi Vaclav,
Just to say to be carefull with formula in Hentz's thesis: the idea
was to use as inputs for contact properties the Young modulus and
Poisson ratio that we want to obtain macroscopically for the granular
assembly. The "funny term" are use to compute kn and ks with respect to
these macroscopic Young modulus and Poisson ratio (The objective was to
avoid a calibration processus). But, actually it doesn't work, this
computation with formula (**) of kn and ks doesn't allow to obtain,
during a triaxial compression for instance, the values of young modulus
and poisson ratio that we expected (or at least if works only for a
given size distribution at a given density for a given confining pressure).
In my opinion, the only important point is to compute kn and ks such as
scale effects are avoided, and I think it is well done in the current
formula (*) in Yade.
Best,
Luc
Václav Šmilauer a écrit :
I am having doubts about correctness of formulas in
Ip2_FrictMat_FrictMat_FrictPhys (I didn't use that for simulations, but
I am trying to relate critical timestep based on kn and p-wave in yade)
In p2_FrictMat_FrictMat_FrictPhys:63
Real Kn = 2*Ea*Da*Eb*Db/(Ea*Da+Eb*Db);
which is HarmonicMean(Ea*Da,Eb*Db) (Da and Db are radii r₁, r₂); if
Da==Db && Ea==Eb, it reduces to
Ea*Da. (*)
I am having Hentz's thesis at hand, which describes algorithms which I
think should be the same. Kn reads like this for Hentz (eq 4.19, pg. 86)
(the funny term to calibrate Poisson's ratio contains fixed-value
coefficients α, β, γ; for average Poisson's ratio 0.25, its value is
1.0):
kn=EA/d₀ * funny_term_equal_to_1.0,
where E=average young's modulus, A=equivalent cross-section of
interaction (which Hentz defines as π*min(r₁,r₂)²), d₀=initial (current)
distance of spheres r₁+r₂. Let's try to do something with that, assuming
r₁=r₂=r for now:
kn=E*A/d₀=E(πr²)/(r+r)=Erπ/2, (**)
which leads me to think, comparing (*) and (**) that in Yade π/2=1,
wherefore π=2. No kidding.
It also means that Ip2_FrictMat_FrictMat_FrictPhys gives stiffness that
is 1.57× smaller than one used by Hentz.
?!
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--
Luc Sibille
Université de Nantes - Laboratoire GeM UMR CNRS
IUT de Saint Nazaire
58, rue Michel-Ange - BP 420
44606 Saint-Nazaire Cedex, France
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