Dear Benhour,

Thank you for taking my point heart and providing more specifics about your 
actual problem.

For the horizontal axis, I have considered the zero displacement along 
> y-axis because of symmetry. Is it correct? Should I fix the center of the 
> circle as well? 

If you don't provide at least one Dirichlet constraint for each of the 
solution components then your problem is indeterminate. So if you only 
constrain the x-DoFs along the y-axis and have no other Dirichlet 
constraints then this could be the source of some troubles. 

> How Can I do that? In other words, How can I fix one point (vertex) in 
> 2-D? 

You have to manually add such a point constraint to the constraint matrix 
or map of boundary values. If your centre point is coincident with a vertex 
of the triangulation then you can achieve this with the help of the 
cell->vertex_dof_index() function. There have been plenty of posts 
in the past on how this function works, so I need not explain it again in 

I should also note that for highly nonlinear problems, if your load 
increment is too large between time steps then this could also be 
problematic (unless you're using a load-following algorithm like the 
arc-length method). It may be of use to reduce the magnitude of the applied 
traction while you're debugging this.


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