Yade

coordinate system, local or global

Asked by ytang

Hi All,

I want to get the macroscale stress of a local area in a sample.
Here are my thoughts.
How to relate the macroscale stress with the microscale stress?
I'm thinking to use the idea of the representative volume element, something like the measurement sphere in PFC.
sigma(macro) = 1/V*sigma(per-particle)
because in YADE, we can get the per-particle stress for each particle[1-2]. so it's very easy to get the macroscale stress for a local area. (#### although we can use the equation: sigma(macro)= 1/V*f*l,where f is the contact force, l is the branch vector.#####)

In[1], it mentioned body stress has three principal stress and the associated principal directions.
In order to use the equation above, I need to add the stress in each direction. I don't know whether the principal directions were in the local coordinate system or the global coordinate system. If they are in the global coordinate system the equation would be easy to calculate. If they are in the local coordinate system, it will be very complex. (convert all the coordinate into global system and then calculate the macroscale stress)

my question is: how can I know the principal directions is in the global or local system?

thanks,
Yong

References:
[1]https://yade-dem.org/doc/yade.wrapper.html?highlight=recorder#yade.wrapper.VTKRecorder
[2]https://yade-dem.org/doc/yade.utils.html?highlight=bodystress#yade._utils.bodyStressTensors

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Jan Stránský
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Jérôme Duriez (jduriez) said : 		#1

Outside special cases (usually related to the description of rotational movements and normally highlighted in the doc), most of YADE stuff is in "global" frame.

That's the case of bodyStressTensors() outputs in particular.

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Best Jan Stránský (honzik) said : 		#2

Hello,

> my question is: how can I know the principal directions is in the global or local system?

all stress components and components of principal directions are saved in global coordinate system.

what do you mean by local coordinate system (there can be many of them)?

> ... principal directions. In order to use the equation above ...
> I need to add the stress in each direction. I don't know whether the principal directions were in the local coordinate system or the global coordinate system.

both "the equation above" and "adding the stress in each direction" has nothing to do with principal directions..
I feel some misunderstanding here..

> it will be very complex. (convert all the coordinate into global system and then calculate the macroscale stress)

just a note, converting coordinate systems is one matrix/quaternion multiplication..

cheers
Jan

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Bruno Chareyre (bruno-chareyre) said : 		#3

> can I know the principal directions is in the global or local system?

Hi,
I'm guessing you refer to the local principal axis of one particle as "local system".
You are then asking if the principal directions are defined in principal frame itself.
In such case the the principal directions would be (1,0,0), (0,1,0), and (0,0,1).
Which would give zero information and be really pointless.
It's enough to sum stresses, no need to worry about principal axis.
Do I miss something?
Bruno

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ytang (ytang116) said : 		#4

Hi Jerome,

So you mean that the principal directions are in the global system?

######################
Hi Jan,

The local system I'm referring is the system on every particle itself.

>>>both "the equation above" and "adding the stress in each direction" has nothing to do with principal directions..

Here I'm thinking that the principal stresses have different principal directions, so if we want to get the overall stresses for RVE, we need to decompose the principal stresses into the global system. So I think we need the principal directions.
#########################
Hi Bruno,
Yeah, I refer to the system on the particle itself is the local system.
As I mentioned before, in order to get the overall stresses for a specified volume, I need to decompose every principal stress into the global x, y, z, axis and then added all the components in each direction so that I can get the overall stresses with three components in the three global directions. this is the reason I want to know whether the principal directions are in the global system or not.

############
overall, with the information, you guys mentioned before. Now, I know that the principal directions are in the global system.

thanks,
Yong

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Jan Stránský (honzik) said : 		#5

Hi,

>> what do you mean by local coordinate system (there can be many of them)?
> The local system I'm referring is the system on every particle itself.

yes, local = on very particle. Still you can define whatever as LCS. W.r.t. original orientation, w.r.t. principal stress, w.r.t surrounding particles, ......
It is not relevant to this discussion any more (as the saved values are in global coordinate system), just a note..

> Here I'm thinking that the principal stresses have different principal directions

yes

> so if we want to get the overall stresses for RVE, we need to decompose the principal stresses into the global system. So I think we need the principal directions.

no, if you want to get overall stress, just sum/average the "ordinary" stress (I assume you have it saved or access to it, because it is anyway needed to compute the principal values/directions) and do not bother with the principal values/directions at all.
(I think somewhere here is the source of the confusion)

Maybe a MWE with a few spheres could help..

cheers
Jan

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ytang (ytang116) said : 		#6

Thanks Jan Stránský, that solved my question.