# yade-users team mailing list archive

## Re: some questions (MacroMicroElasticRelationship)

```> There is no such damping coefficient in current contact laws. There is
> only a numerical damping, called "non-viscous damping" in Cundall's
> papers, which applies at the level of resultant forces and moments on
> each particle (see damping classes).

Okay

> > E = D/S * Kn * ( beta + gamma * Ks/Kn ) / (alpha + Ks/Kn)
> > v = (1 - Ks/Kn) / (alpha + Ks/Kn)/
>
> Is it clear for you that in the equations above *E and v are elastic
> parameters of a sphere packing*, measured in a simulated test?

Now yes :)

> I guess
> alpha, beta, gamma are ad-hoc coefficients that fit the curves obtained
> after a parametric study of E/kn =f(ks/kn) and v=f(ks/kn) in a simulated
> triaxial test (otherwise, i don't see how 3 coefficients can be computed
> from 2 equations!).

> Note that these relations probably depend on the
> compacity of the packing and particle size distribution.

> >
> > Kn = E * S/D * (1 + alpha) / [ beta * (1 + v) + gama * (1 - alpha*v) ]
> > Ks = Kn * (1 - alpha*v) / (1 + v)/
>
> Here, kn and ks are constants stiffness coefficients that WILL give you
> given values of macroscopic elastic moduli Em and vm. Hence, the model
> is not based on Eg, vg of the grains, it is based on Em, vm that you
> want to obtain at the scale of the packing. This is in fact a common
> situation when you want to simulate soil or concrete.

Okay

>
> > where alpha, beta, gamma is the parameters will be identified; E, v is
> > Young's Modulus and Poisson ratio.
> >
> > However, I on former do not understand as they have turned out and how
> > can be used in the linear contact model
> > Fn = kn * xn,
> > Ft = kt * xt
> > where xn - depth penetration, xt - relative tangential displacement.
>
> I'm not sure I understand the problem. If constants kn and ks are
> defined, then you can compute the forces based on
> positions/displacement, there is nothing more here (note that second
> equation is in fact used in an incremental vectorial form : dFt = kt *
> dxt).
>

I considered, that as in a reality dependence between a pressure and
deformation is nonlinear (Hertz), there is no sense (way) to define factors
for linear model (not having, in general, clear physical sense) using
parameters Young and Poisson as the turned out dependence will be far from
real. It is necessary to use empirically defined parameters, that you and do
as I has understood.

>
> The model of interaction in ElasticContactLaw in Yade is linear elastic
> in normal direction, and linear elasto-plastic in tangential direction,
> exactly the same as in most Cundall's papers. The relations with alpha,
> beta, gamma is just a trick to choose the values of kn and ks.

Okay

> Again, to be sure it is clear : there is no dissipation at contact, and
> there is nothing like a restitution coefficient or a priori duration of
> impact in Yade, appart from the ones you can observe in the results of a
> simulation. There is just kn, ks, and numerically damped Newton's laws.
>
> I hope it helps.
> Bruno

Okay. Many thanks, you very much have helped me.

> Frederic Donze

Many thanks, It is interesting to me.

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