# yade-dev team mailing list archive

## Re: [Yade-users] [Question #676841]: the definition of porosity

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As for me, I subscribe to Bruno's presentation: better speak in terms of normal component of relative displacement between centers.
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Jérôme

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Chargé de Recherche / Research Associate
Irstea, RECOVER
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On 17/12/2018 13:43, Bruno Chareyre wrote:
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On 12/17/18 12:14 PM, Jan Stránský wrote:
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yes. In reality (if the particles were soft), there would be no overlap but the particles would deform (being in contact, but not overlapping). In Yade, the particles are rigid and do overlap. Repulsive forces are somehow computed from this overlap. Porosity is computed using the original particles volume. This way, the computation is very easy and fast.
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>From existing overlaps, you can relatively easily compute actual volume
of overlaps and adjust the evaluation if needed.
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I beg to disagree. :)
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It would be better if we could speak the same language in answers (that's why I'm moving the discussion to yade-dev), let's see if we find a common ground. I would suggest that Cundall/Yade DEM makes no assumption of rigidity/overlaps. The notion of overlap is misleading and should be avoided. I usually speak of normal displacement wrt. equilibrium state, instead.
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The only rigid-body approximation is in Newton, where we take moment of inertia constant (it should change with deformation). Deformation is neglected from an inertial point of view, that is true, but it doesn't mean no deformation anywhere.
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In contact models it is admitted that the bodies are not rigid, since there can be relative motion between bodies in contact. Hertz-Mindlin is a perfect example, it is directly accounting for internal deformation, and it is derived on the basis that solid surfaces  *cannot* overlap. The other models can be seen as linearizations of HM, and along this line they don't introduce overlaps either.
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The fact is that we never display deformed shapes of particles. We could in some cases (with HM at least), and then the spheres would appear with surface deflection instead of overlaps. It would be painful to implement and rendering would be much slower, but virtually it can be done. Hence why overlap is just a geometrical artifact. It is not needed in the governing equations, it only appears as a byproduct of graphical display.
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Rejecting the notion of overlap is I think the only way to escape classical ill-posed questions on porosity. "Should overlapped volumes be removed?" If we agree that there is no overlap there is of course no reason to compute overlapping volume. What is the change of volume of a compressed contact then? Well, HM tells you exactly the volume change as part of the closed form solution. If someone is using a linearized form, defining accurate volume change is less clear, it may have to be defined as part of the contact model itself. But in any case, the overlapping volume is irrelevant to physics.
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Bruno

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Also please, if the question is about porosity, next time provide the
code you use to compute porosity. There are two of them, [1] using the
computation you described, the other [2] using voxel approximation (but
for your case, computing actual overlaps is not that difficult and much
more precise).

Jan

[1] https://yade-dem.org/doc/yade.utils.html#yade._utils.porosity
[2] https://yade-dem.org/doc/yade.utils.html#yade._utils.voxelPorosity

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