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Displacement due to point contact

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Hi,
I want to simulate how a planar surface is depressed by the weight of a overlaying sphere (gravity loading) in Structural Mechanics Module. Both sphere and planar surface are expected to be in point contact. First I attempted a 2D version of this problem using circle and a rectangle as shown in attached figure. The bottom boundary of the rectangle is constrained while a body-force is applied on the circle. There is no issue with the mesh. But when I run the Study, Comsol simply gives an error message:
Failed to find a solution.
The relative error (0.69) is greater than the relative tolerance.
Returned solution is not converged.
- Feature: Stationary Solver 1 (sol1/s1)

To finalized the circle and rectangle geometry, I tried both "form union" and form "assembly options" but no success. The problem seems to be the "point-like contact" between the circle and the rectangle which is creating some singularity and preventing the solution from converging. The solution can be made to converge artificially by introducing a small boundary overlap between the circle and the rectangle. This I have tested without any issue by moving the rectangle upwards by a small amount so that there is a finite overlap between circle and rectangle. This also shows that problem is setup correctly. The solution fails only when the two domains are in 'point-like' contact. This is something I did not encounter before. I would like to know if there is robust and fool-proof way to handle point-like contacts/boundaries between the objects in COMSOL? It is possible that I am missing something very trivial, but I would greatly appreciate if any of you could share your valuable insight.
Thank you
Ravinder


2 Replies Last Post Apr 1, 2016, 3:27 p.m. EDT
Henrik Sönnerlind COMSOL Employee

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Posted: 7 years ago Mar 31, 2016, 11:36 a.m. EDT
Hi,

Please check out the model www.comsol.com/model/cylinder-roller-contact-1431 which seems very similar to your example.

Quoted from its documentation:

"To reduce the number of iteration steps and improve convergence, it is good practice
to set an initial contact pressure as close to the anticipated solution as possible. A good
approximation is to use the value of the external pressure—in this case the external
point load divided by an estimated contact length and the thickness. In this example,
it is necessary to specify an initial contact pressure to make the model stable with
respect to the initial conditions, because the initial configuration—where the cylinder
is free to move in the vertical direction—is singular. An alternative could be to define
the geometries with a small overlap or supporting the roller with weak springs."

Regards,
Henrik
Hi, Please check out the model https://www.comsol.com/model/cylinder-roller-contact-1431 which seems very similar to your example. Quoted from its documentation: "To reduce the number of iteration steps and improve convergence, it is good practice to set an initial contact pressure as close to the anticipated solution as possible. A good approximation is to use the value of the external pressure—in this case the external point load divided by an estimated contact length and the thickness. In this example, it is necessary to specify an initial contact pressure to make the model stable with respect to the initial conditions, because the initial configuration—where the cylinder is free to move in the vertical direction—is singular. An alternative could be to define the geometries with a small overlap or supporting the roller with weak springs." Regards, Henrik

Nagi Elabbasi Facebook Reality Labs

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Posted: 7 years ago Apr 1, 2016, 3:27 p.m. EDT
Hi Ravinder,

Following Henrik’s suggestion should resolve the problem. I want to clarify one thing though about “singularity”. If there is no initial contact between the parts then the model stiffness matrix is singular due to the lack of vertical constraints on the sphere. That is the singularity that is most likely causing convergence difficulties, in my experience. It is different from the stress-singularity you referred to that results from point contact.

Nagi Elabbasi
Veryst Engineering
Hi Ravinder, Following Henrik’s suggestion should resolve the problem. I want to clarify one thing though about “singularity”. If there is no initial contact between the parts then the model stiffness matrix is singular due to the lack of vertical constraints on the sphere. That is the singularity that is most likely causing convergence difficulties, in my experience. It is different from the stress-singularity you referred to that results from point contact. Nagi Elabbasi Veryst Engineering

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