Dear all,
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
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