# Normal stiffness define

Hi guys,

I was wondering the normal stiffness in yade is calculated by (https://yade-dem.org/doc/formulation.html#normal-stiffness). And I posted one similar question ( https://answers.launchpad.net/yade/+question/694217) before but I am struggling again for some questions:

1. The normal stiffness of compression and tension is the same in the definition, does that mean the macro-material is one phase? In another word, two particles are connected by cement, if they have the same tension and compression stiffness, does that mean that the cement has the same mechanical properties as particles. However, Assume that cement is very soft and particles are hard, I think the tensile stiffness would be much smaller than compression. So is this situation could be realized by Yade?

Thank u very much.

Cheers,
Aaron

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 Revision history for this message Jan Stránský (honzik) said on 2020-12-13: #1

Hello,

TLTR: the fact that stiffness is same in tension and in compression has influence on "almost nothing".

> And I posted one similar question

normally we try to force separate question for separate question / topic, but here maybe it would have been reasonable to continue at the other thread..

=====
In general:

you have a (let's call it as) micro-mechanical model.
There are several ways how to interpret it (on macro level).
- as particulate material (particles correspond to real grains, interactions correspond to real interactions)
- as continuous material (particles are just artificial discretization, interactions model somehow in discrete manner the continuous stress field)
- as a truss structure (particles has no real interpretation, interactions (network) represent real trusses)
- ...
- ...
- infinitely many other options

Also, there are maaaany options how to model "cement" and consequently how to deal with (not only) this tension/compression stiffness problem.
- grains are modeled by single particle X grains are modeled by multiple particles
- cement is modeled as interactions between grain particles X cement is modeled by particles
- ... again maaany other options and combination of options

> The normal stiffness of compression and tension is the same in the definition, does that mean the macro-material is one phase?

No. At least not necessarily.
The fact that stiffness is the same in tension and compression has no implicit influence on phases (however you define it).
From my point of view, the phases are (should be) more related to stiffness (or other material parameters) VALUES.
See above, you have model, you can interpret it in many ways, including interpretation of phases.

> two particles are connected by cement, if they have the same tension and compression stiffness, does that mean that the cement has the same mechanical properties as particles.

No. At least not necessarily.
The fact that stiffness is same in tension and compression has no influence on the relation of "cement" and "particles" mechanical properties..
Note that in yade, interaction and material of particles may be independent (if you change material of particle, it has no effect on existing interactions).

> Assume that cement is very soft and particles are hard, I think the tensile stiffness would be much smaller than compression.

No. At least not necessarily.
What does "soft" and "hard" exactly mean? Low and high stiffness? Low and high strength?
Anyway, no reasonable "soft" and "hard" definition has influence on different values in tension and compression..

Don't you mix stiffness and strength? Then your concerns would make much more sense..

> So is this situation could be realized by Yade?

There are several options:
- implement a new material model to fit your needs
- model "cement" differently than just by one interaction. E.g. model the cement phase with small particles, some bonded with both connecting "grains", some not. Then naturally stiffness would be different in tension and compression from the "frict phys" nature of non-cohesive parts of the cement.
- ...

But first you should clarify (to yourself) WHAT you want to model. The question seems to be full of confusion and suggests that this step is not yet solved.
"How" step does not make sense before.

cheers
Jan

 Revision history for this message Aaron Liu (voyagening) said on 2020-12-15: #2

Hi Jan,

>What does "soft" and "hard" exactly mean? Low and high stiffness? Low and high strength?
I mean the stiffness here. I see what you mean. We have many ways to represent and model the two-phase (particle and cement).

If I would like to model the cement as the interaction between particles. And let stiffness under compression and tension are different. For example, two particles(E=1e10) are connected and their interaction tension stiffness is 1e4 Pa and compression stiffness is 1e8 pa.
Since 1/(E1.D1)+1/(E2.D2) is used to define the normal stiffness as (https://www.yade-dem.org/doc/yade.wrapper.html#yade.wrapper.Ip2_FrictMat_FrictMat_FrictPhys) described, and the normal stiffness no matter compression and tension is the same and has to be related to E of particles. I am still wondering that is there any ways to define the stiffness of a pair of compression and tension differently and the stiffness is independent to E of particles.

Best,
Aaron

 Revision history for this message Jan Stránský (honzik) said on 2020-12-15: #3

> normal stiffness ... and has to be related to E of particles
> is there any ways ... the stiffness is independent to E of particles

The interaction stiffness **IS** independent of E of particles.
The interaction stiffness **does not need to be** related to E of particles.
If you do nothing about it, the (very reasonable) default behavior is that the interaction stiffness is harmonic mean of particle stiffnesses.
But you have several ways how to make it less or more independent:
- using MatchMaker (if Ip2 supports it) and its "algo" or even "val" to break the dependency
- modifying interaction properties directly, for i in O.interactions: i.phys.kn = whateverDependentOrIndependentValue
- set some particle material, create "default" interactions based on current material, assign different material to the particles (has no effect on existing interactions)
- ... ?

> I am still wondering that is there any ways to define the stiffness of a pair of compression and tension differently

I am afraid a new contact law is necessary..

As you mentioned FrictPhys, it already has different stiffness for tension and compression.
The disadvantage is that the tension stiffness is 0 and cannot be adjusted.. :-)

> If I would like to model the cement as the interaction between particles.

I see two easy approaches. Assuming you have the desired packing, you can

1)
- set real material to particles (particles have "good" properties)
- crate initial cohesive interactions (interactions have "wrong" properties)
- modify interactions to match concrete properties (interactions now have "good" properties)

2)
- set auxiliary "concrete" material to particles (particles have "wrong" properties)
- crate initial cohesive interactions (interactions have "good" properties)
- set real material to particles (particles now have "good" properties)
(recall that changing particles' material has no effect on existing interactions)

cheers
Jan

 Revision history for this message Aaron Liu (voyagening) said on 2020-12-23: #4

Thanks Jan Stránský, that solved my question.