# Stent deployment fails to converge with more components

Hello everyone,

I am trying to simulate a stent expansion with the aid of a balloon, which is simulated as a cylinder in my model. The stent converges successfully when it is comprised of 2 rings (4 symmetrical bodies that share topology) as shown in image (1). However, when I add up more components of the stent, namely 4 rings (8 symmetrical bodies that share topology) as shown in image (2), while maintaining the same constraints, the solution fails to converge short after the balloon touches the stent and some deformation has occurred to the stent.

Are there any suggestions? Allow me to provide any further information needed.

## Comments

Hi Stathis,

Longer stent means it's slender thus more difficult to converge. It will be better if you let the balloon touch the stent initially to make the contact status "closed" initially. It not only saves time but also get rid of many convergence issues caused by contact. You can check the initial contact status by right click on "connections" in the tree outline --> insert --> contact tools.

Regards,

Wenlong

Sir you were right about this one!

I appreciate your contribution!

Kind regards,

Stathis

Mr Wenlong I am afraid that although the model converged with 4 rings, it fails to converge when having 8 rings in total. The goal is 16 rings in total.

Are there any further suggestions or modifications that you would recommend?

Kind regards,

Stathis

Do you have one or more Newton-Raphson Force Residual plots requested under the Solution Information folder?

Please insert an image of the location where the maximum value of Newton-Raphson Force Residual is and make sure the Element Edges are turned on so we can see the mesh.

One corrective action may be to have smaller or better shaped elements at the location of the maximum NR Force Residual.

The maximum value of N-R residuals appears to be here, while the maximum force is 0.016 N.

This is probably because I have separated the stents as shown below (quarter-double rings). The reason why I am doing this is because the multizone mesh is difficult to be implemented on the geometry as 1 body. It takes too much time to mesh it and sometimes the engine fails. So, what I did was merging the mutual nodes of the different bodies.

Slicing up the stent into many small parts is a good idea because the meshing is more robust and much faster. When you are done meshing, the nodes should line up at the cut faces, then Mesh Merge is a very robust way to connect the mesh. That is all good. The convergence problem has to do with how many elements are across the width and through the thickness at that junction.

Zoom in on the mesh in the problem area, I can't see the elements. Show the elements undeformed in the mesh, not in dark blue because that makes it hard to see the elements.

I apologize about that.

You only have one element through the thickness of the stent. That is inadequate. Change the mesh to get two elements through the thickness and at least two elements across the width. Below is an example of a 2x2 mesh. If you don't get convergence, increase to a 3x3 mesh.

Peteroznewman has made a good point: when you have a longer stent the bending behavior becomes more obvious, and it becomes more important to have several solid elements through the thickness direction to capture the bending behavior well.

I would like to thank you about the time you take to answer my questions! Your help is truly valuable.

Currently I am working on a denser mesh.

Regarding the constraints, do you think that setting a

remote displacementto the4surfacesbellow, with0 rotation and translationon theXaxis, is the most sufficient and quickly converging way of constraining the problem? To make things clear, all of those 4 surfaces are parallel to the Y-Z system.Kind regards,

Stathis

Based on a model I've tested, directly applying a displacement constraint seems easier to converge. To do that, you can create a local polar coordinate system and constrain the axial movement and rotation movement of these 4 surfaces, and allow the movement in the radial direction.

Regards,

Wenlong

I don't know if I misunderstood something but if the radial axis is the only free axis, the geometry is naturally going to deform on these 4 surfaces to maintain radial displacements. Isn't that unwanted?

Stat,

I agree with Wenlong, but I would constrain exactly 3 vertices, spaced 120 degrees around the stent circumference in the same Z plane.

Create a Cylindrical Coordinate System at the center of the stent with the Z axis along the stent axis.

Insert a Displacement BC and

make sure you select the Cylindrical system.On each of the 3 vertices, leave X = Free, Y = 0 and Z = 0. That is radial = free, theta = 0 and Z = 0.

This is a kinematic connection to ground. That means if you were to do a thermal expansion, there would be zero stress induced by this connection to ground.

Hi Stat,

I think peteroznewman's approach is better: instead of constraining 4 surfaces, only constrain 3 vertices, and in this way these 4 surfaces can also have deformation (like small rotation to make it out of yz plane).

I may not understand your question correctly. You do want to constraint the axial and rotational DOF and let it expand freely in the radial direction, right?

Regards,

Wenlong

Yes this is correct! Unfortunately I can't find 120 degrees spaced vertices, so I will constraint 4 of them spaced 90 degrees each.

Regarding the 8 rings-model, the denser mesh did not seem to have significant improvement over convergence. Using a 3x2 mesh structure, the model failed to converge relatively early as shown below.

Stat, don't use 4 vertices, that is an overconstraint. You need exactly 6 constraints to connect a body to ground. Two constraints each on 3 vertices equals 6 constraints. If you add a fourth vertex, that is 2 constraints too many.

Just use 3 vertices. They don't have to be at 120 degrees, they can be at 90 degrees. The stent will still expand around the central axis because that is where the cylindrical coordinate system is.

On a perfectly symmetrical part, the extra vertex may not be in conflict with the other three vertices, so you might not see a difference, but on a non-symmetric part, you shouldn't use 4 vertices.

With 3 vertices constrained as suggested above and some tweaks on the contact parameters the 8-ring model converged with a 2 x 1 mesh. I will report the outcome of the 16-rings model when the analysis is done.

Again, I want to thank both of you for the time you devoted.

Kind regards,

Stathis

The 16-ring model failed to converge with a 2x1 mesh but converged successfully with a 2x2 mesh as you suggested!