yade-dev team mailing list archive

[Václav Šmilauer <eudoxos@xxxxxxxx>]

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.

?!