# Are polyhedra aggregates of spheres?

Asked by Damiana Catanoso on 2019-06-21

Good evening,

I am considering using Yade for a project for which I need to simulate large pieces of ice breaking under certain forces. The idea is to start with a large polyhedron shape which breaks into smaller polyhedra under compression forces. This has been done with Yade before https://www.youtube.com/watch?v=IjXvPLU92xQ&t=1s. If I understood correctly, two criteria to establish if the initial polyhedron breaks have been implemented before: the Mohr-Coulomb and MaxTau principles. In order to check where the crack starts in the initial polyhedron and in which direction it propagates, the algorithm should know what is the sigma-distribution along the body.

So my questions are:
- how does the algorithm decide in which point the material breaks and how the crack propagates in 3D?
- What is the internal structure of the polygon? Is it made of spheres (in this case the sigma-forces would be given by the sphere-sphere contact forces)?

Thank you and best regards,

Damiana Catanoso

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2019-06-27
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2019-06-26
 Jan Stránský (honzik) said on 2019-06-22: #1

Hi Damiana,

> I am considering using Yade for a project for which I need to simulate large pieces of ice breaking under certain forces. The idea is to start with a large polyhedron shape which breaks into smaller polyhedra under compression forces

One option is, as described, to use one big particle and then split it.
The other option is to use an "agglomerate" approach where the ice is approximated by (possibly spherical) cohesive particles .

In general (as always :-) the proper choice depends on many factors (geometry, loading type, expected failure mode and results, ...)
Could you share some more details about the project?
Why do you want to use Yade/DEM and not another method (FEM)?

> two criteria to establish if the initial polyhedron breaks have been implemented before: the Mohr-Coulomb and MaxTau principles

the "plain" PolyhedraSplitter [1] is the third one

> how does the algorithm decide in which point the material breaks and how the crack propagates in 3D?

After a quick look, it seems that all the methods uses b.state.pos (basically center of mass of th epolyhedron) as the point of the split.
What "propagates" mean? Currently there is no propagation, just creating the crack at once.
If you mean the orientation of the crack, it is one or two planes plane(s) based on principal directions of the approximated overall stress tensor (we can point you to the code/references if you want/need).

In general, arbitrary condition/method could be defined.

> What is the internal structure of the polygon? Is it made of spheres (in this case the sigma-forces would be given by the sphere-sphere contact forces)?

I assume polygon = polyhedron.
Polyhedron has no internal structure, it is just a polyhedron.
Stress is approximated from contact forces with other bodies using Love-Weber formula [2,3].
The splitting is just "replacing on polyhedron with its sub-bodies", actually modification of dimensions of the original body to be one of its split sub-bodies and adding the other new split sub-body/ies.

cheers
Jan

 Damiana Catanoso (damianacatanoso) said on 2019-06-24: #2

Hi Jan,

Thank you very much, this is very helpful information: all aspects about polyhedra are now clear.

>In general (as always :-) the proper choice depends on many factors (geometry, loading type, expected failure mode and results, ...)
Could you share some more details about the project?
Why do you want to use Yade/DEM and not another method (FEM)?

The scenario I have to simulate consists of: 1) drilling into a large piece of ice and create ice fragments, then 2) scooping the ice. The idea is to couple Yade with Gazebo (ROS), where I will have the model of the robot executing the two tasks with two different end effectors. I want to use Yade for the drilling + scooping phases. In particular, for the drilling phase use a polyhedron, applying brief and intense compression forces until it breaks into sub-polyhedra. Then repeat the process until I get small polyhedra of the desired size. Then switch to a sphere-approach for the scooping simulation (to reduce computational cost) where the small polyhedra are discarded and replaced with small clumps of spheres. FEM would just simulate the ice-breaking process, which is just one part of the project.

>One option is, as described, to use one big particle and then split it.
The other option is to use an "agglomerate" approach where the ice is approximated by (possibly spherical) cohesive particles.

I would like to explore the "agglomerate" option as well. If I simulate the piece of ice using an agglomerate of spheres, is it possible to create bounds between particles which break under compression forces according to the given failure criteria? I saw examples on how to build particles clumps but I didn't find examples where the single clump breaks into multiple clumps, which is what I need.

Thank you again for answering so quickly and efficiently!

Best,

Damiana

 Robert Caulk (rcaulk) said on 2019-06-26: #3

You are probably looking for the JointedCohesiveFrictional model [1][2].

 Damiana Catanoso (damianacatanoso) said on 2019-06-27: #4

Robert, that helps a lot, thank you!