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Message #08256
Re: [Question #235934]: Reference for coeff of restitution in HertzMindlin with nonlinear damping
Question #235934 on Yade changed:
https://answers.launchpad.net/yade/+question/235934
Status: Answered => Solved
Václav Šmilauer confirmed that the question is solved:
The
http://people.ds.cam.ac.uk/jae1001/CUS/research/pfizer/Antypov_Elliott_EPL_2011.pdf
paper gives the same equation under eqs (10) and (17) (though written a
bit differently). I suspect that this paper is the source for the
equation in Yade, since they cite Tsuji 1992 specifically as *not*
giving analytical relationship for alpha(epsilon).
They discuss something just before the end of the paper ("Model
choice"): the contact can be terminated when either the overlap reaches
zero, or when the force is zero. With viscosity, there may be
(unphysical) attractive force while there is still overlap, which might
account for the extra dissipated energy.
I tried to limit (elastic+viscous) force to zero (so that there is no
attraction due to viscosity). The plot is at http://flux.doxos.eu
/spherewallhertz.pdf : I get the energy balance almost exactly (max
kinetic energy before the impact 5200J, after the impact, 3900J is
dissipated by the viscous force, which makes exactly
(52003900)/5200=0.25=0.5^2. The sphere rebounds from 1m to 0.27m, the
still position is at 0.01315, giving coefficient of restitution of
about sqrt(0.27+0.01315)=0.53. The 0.5 vs. 0.53 could be just my
imprecise reading from plots, I assume.
I also tested collision time, which is given analytically in the paper
above (eq (23)) and it agrees with simulation at different impact
velocities (max. 1% difference).
I use Woo code now, but as far as I see, it should be equivalent to the
code in Yade, except for the noAttraction flag mentioned above 
http://bazaar.launchpad.net/~eudoxos/woo/trunk/view/head:/pkg/dem/Hertz.cpp
.

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