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[EDEM] What is cross section area and contact point in 'Fibers bonding model'

Hi,

I’m currently working with the Fiber Bonding model and had a few questions regarding the stiffness calculation described in the documentation.

Let’s consider a case where sphero-cylindrical particles are like below.

Let’s consider a case where this sphero-cylindrical particles are aligned in a straight line and arranged so that they overlap exactly by their radius, as illustrated in the attached image. In this case i have some questions.

Cross-sectional area:
According to the documentation ( figure below ) , stiffness depends on the cross-sectional area of the bonded region. In the configuration above, is it correct to assume that the cross-sectional area refers to the orange line segment area in the image, and therefore its value would be π·r², where r is the radius of the sphero-cylinder?
I would appreciate clarification on how this area is defined in your model.

2. d₁ and d₂ values (distances from the particle centers to the contact point):

In the stiffness formula, how is the contact point defined in this type of overlapping configuration? Knowing this would help determine d₁ and d₂ more precisely.

3. Beam Interpretation in Multi-Contact Particles:

The documentation states:
“The bond emulates the flexibility of the adjacent particles, from their center to the contact point, originating from the theory of beams.”
Given this, can we interpret that in the case of a meta-particle connected to two neighboring particles (left and right), each sphero-cylinder effectively forms two beam elements, one to each adjacent particle?
In other words, would it be physically reasonable to assume that the configuration shown in the attached bottom image, with a particle flexing between two neighbors, is supported by the Fiber Bonding model?

Lastly, is there a detailed tutorial that walks through the entire process of building a simulation using the Fiber Bonding model?

Thank you very much for your time and support. I look forward to your clarification on these points.

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Accepted answers

MA_Celigueta

Hello,
This is Miguel from EDEM team.
I will try to go through all your questions number by number:

1. Yes, the cross section used, when a spherocylinder is bonded, is the cross section of the spherocylinder, exactly as you pointed out: π·r², where r is the radius of the sphero-cylinder. For multi-spheres, it is the cross section of the bonded sub-sphere.

2. At the time when the bond is formed, this model asks EDEM where the contact point is. This means that the contact point is exactly the same you would have in, say, Hertz-Mindlin. From then on, the model remembers where that point is, as seen by particle 1 and particle 2. When there is relative movement between particles, these two points can separate in space, but the model tries to return them to a coincident position with the appropriate stiffness. d₁ and d₂ are the projections of [the vectors from the particle centers to the contact points] onto [the main directions of the sphero-cylinders].

3. Yes. One of the main applications of this model is to bond the particles in a meta-particle. As long as there's contact between them, they will be bonded when the meta-particle is created. The fragment in the docs you were metioning tries to explain that one same fiber (meta-particle, for example) made of 100 short elements or 10 short elements should have approximately the same bending response with this model, because the length of the particles is included in the equations (question 2). Similarly to Finite Elements, more resolution means more accuracy.

4. I am not sure there's a public tutorial for the Fibers Bonding. I know the team has some examples that could be shared, but I suspect no official tutorial has been prepared yet, as it is a pretty recent model. If I find one I'll post it here.

Do not hesitate to ask anything that is not clear enough.

MA_Celigueta

Hello,
Thanks for providing more details, here are some extra comments:
1- If two sphero-cylinders have less overlap, and the contact area has r' as a radius, then we still use the cross section of the sphero-cylinder. This is because the model is not focusing on the bond zone, but the particle itself is contributing to estimate stiffness. The amount of overlap probably changes d₁ and d₂ but not the cross section or the inertia values.
2- It is right that in the second picture there is a contact surface instead of a point. In that case, EDEM treats that contact as two half-spheres in contact and the contact point lies on the line joining the virtual half-sphere centers.
3- No, particles cannot bend themselves. Despite our claim that we introduce the flexibility of the particle in the bond, what we mean is that the particle is rigid and the stiffness of the bond is lower when the particle is longer. That means that one fiber made of short sphero-cylinders will have higher bond stiffness than one fiber made of long sphero-cylinders, but the stresses and the global deformation should be similar because the relative rotations and displacements between two short particles will be smaller than those between two long particles.

All comments

MA_Celigueta

KJHSNU

Thank you so much for your kind and detailed answeres!

I have some additional questions here.

1.
First of all, regarding my first question, I understand that when the circular parts of the sphero-cylinder are completely overlapping, the contact area corresponds to the radius of the sphero-cylinder. However, I am also curious whether, in the case where two particles are in contact as shown in the figure below, the contact area is still calculated as πr², or if it should be πr’² instead.
Based on the explanation, especially the part that says, “For multi-spheres, it is the cross section of the bonded sub-sphere,” it seems that the contact area would be πr’². Could you please confirm if my understanding is correct?

In addition, I believe that in contact situations commonly observed in DEM, such as the one shown in the photo below, the contact point can be clearly defined as a single point (x).

However, in cases where cylinders overlap as depicted in the lower figure, the contact area becomes a surface rather than a single point. In such cases, I would like to ask how the contact point is defined.

Additionally, I would like to clarify my question once more, as I am concerned that the diagram and my previous explanation may have caused some confusion.
My inquiry is not about whether bending is possible between neighboring particles, but rather whether a single particle itself can be curved or bent.
In the structure shown in the photo, it is not a case of two connected particles, but rather a question of whether a single particle can form a curve, as if it is bending by itself.
From my understanding of the documentation, when another particle is attached to each end of a single particle, a beam element is created at each connection point. ( beam element 1 & 2 is included in one single particle)
Therefore, I would like to ask whether it is possible for a single particle to possess curvature and bend on its own, as illustrated in the third diagram of my question.

Thank you for your support and thank you in advance!

Regards.

MA_Celigueta

KJHSNU

Thank you so much!!

It really made everything clear!

Thank you.😀