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[Chiara Modenese <question232351@xxxxxxxxxxxxxxxxxxxxx>]

Question #232351 on Yade changed:
https://answers.launchpad.net/yade/+question/232351

Chiara Modenese posted a new comment:
Hi Alexander,

Yes, you are right beta_n should be called damping ratio rather than
damping coefficient but you get the concept. Feel free to adjust the text
if you want.

At the time I set the code so that e_n and e_s would be the defined the
same was for convenience but also because I believe that the equation for
alpha was derived for normal impact tests only (please correct me if I am
wrong as I do not have that paper with me right now).

Looking back at this problem, I would not use this form of non-linear
damping because actually the relationship for alpha that is implemented is
not formally correct. It is a good first approximation but analytically is
not consistent (I will see later if I can find the reference that proves
that for you) - if you do some research on the topic you will find
different relationships for alpha.

Chiara


On 6 November 2013 14:16, Alexander Eulitz [Eugen] <
question232351@xxxxxxxxxxxxxxxxxxxxx> wrote:

> Question #232351 on Yade changed:
> https://answers.launchpad.net/yade/+question/232351
>
> Alexander Eulitz [Eugen] posted a new comment:
> Hi, I'd like to reopen this question.
> The Hertz Mindlin contact law allows for two diffrent kinds of viscouse
> damping, i.e. linear and non-linear.
>
> Considering the linear case:
> according to [1] beta_n is the viscous damping coefficient. But how is it
> defined? I did not find a satisfying answer. I looked at [3] and the named
> source from Schwager as wells as at [5], but I do not get it.
>
> In the source of the Hertz Mindlin Contact law [2] beta_n will be used to
> calculate c_n:
>  cn = Cn_crit*phys->betan; // Damping normal coefficient
>
> with Cn_crit being the critical damping coefficient. I recognized that
> rearranging the equation for the damping ratio [4] gives:
> damping_coeff=damp_ratio*crit_damp_coeff which equals the line from the
> source code.
> If this is right, then beta_n is the damping ratio and not a viscous
> damping coefficient.
>
> May second question concerns non-linear viscous damping:
> It is not commented in the documentation [1] but looking at the sources
> [6] tells me that I can enable this kind of damping by specifying the
> coefficients of restitution (en, es). This way a value alpha will be
> computed from it.
> The first strange thing is, that it does not matter whether I specify en
> or es, only en will be used for alpha computation.
> The second strange thing is that the documentation on [1] says:
>  " If e_n is given, MindlinPhys.betan is computed using \beta_n=-(\log
> e_n)/\sqrt{\pi^2+(\log e_n)^2}. The same applies to e_s."
>
> But this is not what is done in the source.
>
> Could you please help me?
>
> [1]
> https://yade-dem.org/doc/yade.wrapper.html?highlight=mindlin#yade.wrapper.Ip2_FrictMat_FrictMat_MindlinPhys
> [2]
> https://github.com/yade/trunk/blob/master/pkg/dem/HertzMindlin.cpp?source=cc#L316
> [3] https://answers.launchpad.net/yade/+question/235934
> [4] http://en.wikipedia.org/wiki/Damping_ratio
> [5] http://woodem.eu/doc/theory/contact/hertzian.html#viscous-damping
> [6]
> https://github.com/yade/trunk/blob/master/pkg/dem/HertzMindlin.cpp?source=cc#L86
>
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