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

```Hi Bruno,

A) I am currently not so active contributor, so I do not insist on my point
of view
B) I like my point of view very much :-) and it makes to me much more sense
and I wanted to present it here

as I understand DEM and always explained it is that:
1) DEM represents material as a set of perfectly rigid particles whose
motion is governed by Newton's second law.
2) Based on particles' mutual motion, interparticle forces are computed
according to constitutive laws.
3) Just after there would be a picture of overlapping particles emphasizing
the overlapping volume/area and explanation that in reality there would be
no overlap but a repulsive force, which is computed by the constitutive law
somehow according to that overlap
4) Interparticle forces are put into equations of motion and numerically
integrated.
5) final note that DEM is "nothing more" :-) and that very large amount of
variants are formed using different particle shapes, constitutive laws and
some other extensions (bonded particles.....)

I think it is dual to the point of view presented by you and they are
nicely interchangable.
However, I think my point of view is more natural and easier to understand
and accept some other assumptions.

The fact that deformations are not plotted nor taken into account in
NewtonIntegrator IMO supports my point of view.

> It would be better if we could speak the same language in answers

100% agreement

> I would suggest that Cundall/Yade DEM makes no assumption of
rigidity/overlaps.

but does not make any assumption on non-rigidity at the same time, right?
:-)

> The notion of overlap is misleading and should be avoided. I usually
speak of normal displacement wrt. equilibrium state, instead.

This applies to spherical shapes. More general shapes can change their
overlap just by rotation.
On the other hand, rigid particles assumption and word overlap express
exactly what one (or at least me :-) would expect.

> In contact models it is admitted that the bodies are not rigid, since
there can be relative motion between bodies in contact.

Relative motion between bodies says nothing about (non)rigidity of the
bodies, or?

> 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.

see point 3) at the beginning. This can be also achieved using the dual
approach: assuming the particles rigid, but computing the force under
assumption that in reality there would be no overlap.

> 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.

Or a dual view: particle overlap is intrinsic feature of the method and
deformation just computational artifact :-) which can easily be done in a
post-processing stage.

> Rejecting the notion of overlap is I think the only way to escape
classical ill-posed questions on porosity. "Should overlapped volumes be
removed?"

Such question always needs a close context. Missing context is IMO making
it most ill-posed.
- I have a loose packing and by some normal compression make it denser. Do
I need to bother with overlaps while computing porosite? Most likely not
- I have a dense assembly by triaxial compression I squeeze it ti 2/3 of
its original volume.. probably in this case it makes sense to somehow treat
overlap/deformation.

> 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.

Well, you always have some limit on accuracy.
HM tells the volume change for one sphere-sphere contact, but many contacts
with "big" overlaps would influence each other and you again ends with an
approximation.
I see three levels of usage (depending on context):
a) you don't take into account overlaps/deformation at all
b) you compute exactly "geometrical" porosity (applicable only on rigid
body assumption) excluding the overlapping volume of rigid particles
c) you compute porosity based on constitutive law (which may be HM based or
may fall to case b) "by default")

> But in any case, the overlapping volume is irrelevant to physics.

Yes. But in "my" point of view, it is an input for the constitutive law :-)

Cheers
Jan
```