# yade-users team mailing list archive

## Re: some questions (MacroMicroElasticRelationship)

```I have found in the Annual Report 2006 of Discrete Element Group for Hazard
Mitigation, page E5
(http://geo.hmg.inpg.fr/frederic/Discrete_Element_Group_FVD.html) expressions
for kn, ks:

if

E = D/S * Kn * ( beta + gamma * Ks/Kn ) / (alpha + Ks/Kn)
v = (1 - Ks/Kn) / (alpha + Ks/Kn)

hence

Kn = E * S/D * (1 + alpha) / [ beta * (1 + v) + gama * (1 - alpha*v) ]
Ks = Kn * (1 - alpha*v) / (1 + v)

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 interested to that I write the PhD thesis about modelling the granulated
materials in which there is a review of various models of interaction: linear
and nonlinear viscoelastic models (Cundall*Strack, Kuwabara&Kono),
Hertz theory, elastoplastic models (Walton&Braun, Thronton), linear and
nonlinear tangential interaction (Mindlin&Derisevich, Walton&Braun).

In the linear models factors of elasticity and dissipation are deduced from
the decision of the differential equation of pair interaction and
__empirically__ defined parameters, such as coefficient of restitution and
duration of pair impact. In the nonlinear models constructed on the basis of
the theory of elasticity Hertz, the given parameters define on the basis of
__clearly interpreted physical parameters__ of a body: the Young's Modulus
and Poisson's ratio.

Therefore it was very interesting to me to learn how it is possible to use
Young and Poisson in the simple and attractive to calculations linear models
of interaction.
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