# yade-users team mailing list archive

## [Question #235934]: Reference for coeff of restitution in Hertz-Mindlin with non-linear damping

```New question #235934 on Yade:

I use the simple-scene-plot.py script to test the coefficient of restition for viscous contact laws, only replacing the two lines in the InteractionLoop with

[Ip2_FrictMat_FrictMat_MindlinPhys(en=.5)],
[Law2_ScGeom_MindlinPhys_Mindlin()],

and setting NewtonIntegrator(damping=0.,...).

The scene is a sphere in free fall onto a box, then rebounding, falling down again etc, until all energy is dissipated. According to the documentation and source code, *en* is the normal coefficient of restitution, so I expect to see the energy quartered (1/4=.5^2) after each rebound. The sphere is originally with v=0 at z=2, entering in contact with the box when z=1.5. Therefore, after one rebound, it should fly up to about 1.625 etc, eventually approaching 1.5.

In the simulation, the sphere peaks at about z=1.55 after the first rebound. Considering that the equilibrium position will be at about z=1.45 due to still weight of the sphere in gravity, I still obtain coefficient of restitution of about sqrt((1.55-1.45)/(2-1.45))=.42, not 0.5.

The source (pkg/dem/HertzMindlin.cpp, lines 89 and 320) references some (Tsuji, 1992) paper for computing the viscous coefficient from the coefficient of restitution (cn=alpha*sqrt(mbar), with alpha=-sqrt(5/6.)*2*log(en)/sqrt(log(en)^2)+M_PI^2)*sqrt(2*E*sqrt(R) and mbar=(m1*m2)/(m1+m2)). I am not able to identify this paper, can I ask for a full reference (e-mailing fulltext is highly appreciated)?

How reliable is this code in Yade? Has someone double-checked that it does what it should?

Cheers, Václav

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