# yade-users team mailing list archive

## Re: the relationship of poisson ratio and tangential stiffness

```Hello,

particle (sphere to be more concrete) modeling of materials with Poisson's ratio over 0.25 is a bit tricky.. I have done a study on it, and (using uniform sphere radius and random dense pack) the only chance seems to define zero shear stiffness and to have low interaction radius (enlargeFactor of BoundDispatcher and InteractionDispatcher), see the last graphs in
However, if another particle shape, nonuniform radius or different packing were used, the results could be different :-)
cheers
Jan
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> Od: "焦利青" <jiaoliqing@xxxxxxx>
> Datum: 21.09.2010 04:24
> Předmět: Re: [Yade-users] the relationship of poisson ratio and tangential stiffness
>
>Hello Vaclav,
>
>From Eq(3.39) and the chart on page 52 in your thesis, How to deal with the kind of materials which have the poisson's ratio of over 0.25 (0.25-0.5). For this kind of materials. In the other words, how to get the Kt from Kn and poisson's ratio? Thank you so much.
>
>Best
>Liqing
>
>At 2010-09-20 23:14:39，"Vaclav Smilauer" <eudoxos@xxxxxxxx> wrote:
>
>>> Thank you for your comments. I can understand it. You know, from the
>>> mechanical concept, the shear modulus (G) can be represented by E/2*(1
>>> +v) for homogeneous isotropic materials, here E is young modulus, v is
>>> poisson ratio. So, can we decide G_over_E is equal to 1/2*(1+v)
>>> directly? Can we use 1/2*(1+v) to calculate kt/kn?
>>> Thank you so much.
>>
>>No, I don't think that would work; the notation in the code (G_over_E)
>>is a little misleading again, G=kt/A and E=kn/A on the interaction level
>>are different from Young and shear modulus for continuum (in the sense
>>of how a RVE of particles would behave globally), depending on packing
>>configuration etc.
>>
>>Eq (3.39), pg 51 of my thesis gives some a relationship between kt/kn
>>and Poisson's ratio based on the microplane theory analogy (see the
>>article referenced for details), but there is a number of suppositions,
>>such as fixed particle radius (otherwise the dimensional analysis would
>>have to take in account more parameters). (pg 52 shows that it matches
>>in a sense)
>>
>>HTH, Vaclav
>>
>>
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