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Local coordinate system for material properties
Posted Apr 22, 2013, 11:34 a.m. EDT Geometry, Materials, Modeling Tools & Definitions, Structural Mechanics Version 4.3, Version 4.3a 3 Replies
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we are trying to do an eigenfrequency analysis of a car tire and are struggling with defining the correct elastic material properties for the tire plies.
The tire plies are fibrous composites consisting of steel cords embedded in a rubber matrix. The steel coords are aligned at a certain, non-zero, angle with respect to the tire circumference (see the attached image), meaning that the ply is anisotropic with respect to the tire's coordinate system. It is no problem to calculate the anisotropic elasticity matrix, but, and here comes my problem, this matrix will be in reference to the local coordinates of the plane the ply lies in. As an example in the picture this local plane is more or less vertical for the tire sidewalls while it is horizontal for the tread area. Additionally, this plane obviously also rotates around the tire in circumferential direction.
Is there a way in COMSOL Multiphysics to define material properties with respect to such a local coordinate system? As far as I see it, I cannot simply use a rotated coordinate system because this is with respect to a global coordinate system, i.e. if I have a correctly rotated system at 0º on the tire circumference, the rotated system will have the same orientation at 90º on the tire circumference, while what I need would there would also be rotated by 90º.
If the tire was just a ring, I might be able to use a spherical coordinate system for this, but as far as I see it, the sidewalls prevent this. In the end, because of the slightly deformed doubly-curved shape of the tire I do not see any easy solution for this based on a global coordinate system.
Any help appreciated,
Carsten
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You have also the default local boundary coordinate system, that follow the boundaries i.e. of your steel wires.
Remains how to project the boundary coordinates onto the full wire domain, or section.
There was a thread about 1-2 months ago (at least this year, I believe) where some of the COMSOL people gave some clues on how to use local boundaries.
Try a search, unfortunately I havent tried this out, but would be very interested to know, so pls report back if you find the "good" way
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Good luck
Ivar
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thank you for the hint, I will have a look for that thread. Actually using the Boundary coordinate system was the first idea I had, but then I realized that it cannot be used inside the material section.
I also realized that I was a little bit in a hurry yesterday, when I wrote the post, so I am not sure if I was really clear about the problem. Since I am not modeling the steel wires explicitly, the problem actually could be simply described as that I need to be able to define the elasticity matrix with respect to a coordinate system which follows what could be called the "neutral line" of the tyre construction, see attached file. Basically, this system would be defined by the two tangential directions and the normal at a given point on the tyre.
/Carsten
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you don't happen to remember anything more specific about the thread you mentioned? I seem unable to find it using the rather limited search options here in forums.
/Carsten