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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