# Constraining displacement in polar coordinates

I am trying to deploy a simple section of a stent geometry using a balloon. I have defined a polar coordinate system for which I displace the balloon in the radial direction. This deforms the stent. The boundary conditions I have set on the stent is to fix the proximal end axially and prevent tangential displacement at the distal end. The remaining struts are also constrained in the tangential direction. The whole body is free to move in the radial direction allowing increase in diameter.

The difficulty I am having is defining the tangential displacement boundary conditions. While it appears to work correctly on the repeating struts, the deformation is not expected on the far end. I have tried various different boundary conditions but all with the same effect. Applying no boundary condition at the distal end causes large contact separation which is not expected in this model. I have tried applying the tangential constraint to a nodal selection, a few nodes only and the whole face.

I have attached an image of the results I get when applying the boundary conditions listed above and constraining the whole distal face in the tangential direction. I will also include the workbench file in a comment to this thread

Any help would be greatly appreciated.

Thanks

J

## Comments

The bow-tie shape of the elements on the end of the stent shown in the lower image is called hourglass mode.

An hourglass stiffness factor is typically available for elements to help eliminate the hourglass modes. If required, the user must check to see that the artificial energy due to hourglass control stiffness is a small (< 5%) percentage of the total stiffness energy.

In ANSYS, the hourglass stiffness factor is defined using REAL constant HGSTF, the artificial energy can be plotted using PLESOL,AENE, and the total stiffness energy using PLESOL,SENE.

For SOLID185 Real Constants

HGSTF - Hourglass Stiffness Scaling factor if KEYOPT(2) = 1 (Default is 1.0; any positive number is valid. If set to 0.0, value is automatically reset to 1.0.)

Try using a HGSTF scale factor bigger than 1 such as 2 or 10.

Hi Peter,

Thank you for your quick response, I have been able to solve the issue and successfully simulated the deployment of the whole stent by constraining the displacement in the three polar directions.

I am now trying to deploy the stent using a balloon/using pressure applied normal to the inner cylindrical face. In both scenarios I have the middle struts constrained tangentially and one end fixed in the axial direction. I know during the expansion using displacement the expansion would be uniform in the radial direction and all nodes would expand by the same amount. However when I remove the condition and simulate with either pressure or the balloon, the free/unconstrained end expands significantly more than the fixed end (see figure). I know the nodes may not stay perfectly in plane with their neighbours, but this result is not expected.

I have also included the outcome when using the balloon for reference. I am aware my contact setup is not perfect in this but it shows the same deformation at the free end suggesting contact is not the only issue.

To understand the cause of this I have tried to simplify the model further to just a quarter cylinder with an end fixed in tangential and radial directions. Similar deformations are visible (see figure below)

I get these two warnings as soon as I remove the radial displacement discussed in the original post.

With the second warning I understand that not have a constraint in all directions would make the model underconstrained. However I cannot constrain any nodes in the radial direction otherwise the radial expansion would not be correct.

Do you have any idea why pressure would cause the results seen?

Many Thanks!

J