Surface contact?

Question

Hi,

I want to use FENiCS for simulating heart valves and was wondering if it is possible to include surface to surface (deformable) contact? I will appreciate any help.

Also, for a thin shell model, I am sure it can be done but can someone point to an example?

Thanks in advance!
Ankush.

Answer 1

You may definitely employ interior facet integrals and deform a mesh in FEniCS if this is the point.

Comments

Hi Jan,

Thanks for your reply. I am only starting to use FENiCS, so I may lack some background on your answer. Can you explain a little more? Is there an example I can follow?

I think I want to use something along the lines of a penalty or augmented Lagrange method for the contact. If it is largely going to be manual, searching for contact might be the hardest part.

Thanks!

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With weak constraints (Lagrange multipliers) on subdomains, there is still a problem that FEniCS does not support mixing form arguments defined on different meshes. There is available workaround to restrict Lagrange multiplier by DirichletBC on all the redundant DOFs but this is not optimal. Note that multidomain support is on plans. But I'm not sure if this limitation has direct implications to penalty or Augmented Lagrangians method.

I'm not sure at all how do you want to handle a contact, if by fitted mesh or some level-set treatment. Former is probably possible. Regarding latter there was some attempt (PUM compiler, PUM library) to implement XFEM/PUM method, but this is now deprecated and reimplementation is on developers' plans. But it may be interesting to look on PUM compiler/library as it was mainly targeted on fracture mechanics I think. Another possibility is some phase-field model, isn't it?

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I am not entirely following what you mentioned. I guess because my experience with FENiCS is almost zero. Solving contact with full Lagrange is usually unstable because of min-max problem, that's why I think penalty/augmented Lagrange will be appropriate.

I am not using level-set. There are only two surface meshes and I want to include the contact between them. Given the simplicity of the problem, I don't see the need for PUM or phase-field models.

Thanks!

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Never mind. I'm just saying that mixed functions spaces currently does not support mixing on different meshes. But for penalty / augmented Lagrangians you probably do not need forms defined on mixed function space involving penalty (and eventually multiplier approximation) as these are explicitly calculated each iteration. Simply these are not form arguments but only coefficients which can be definitely from different mesh.

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I see. So, do you mean that currently contact using penalty is not possible in FEniCS?

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I'm not sure what do you mean by a contact, but interior surface integral involving penalty coefficient is possible.

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I'm sorry I should have explained that. In solid mechanics, lets say I am modelling two shell surfaces. Upon application of pressure they deform which might make them intersect. To avoid this non-physical situation, usually a "contact" is added to models. Penalty methods works such that if the surfaces are close enough at a time point, they experience a force to avoid them intersecting at all. So, there are two parts to this:

1) Determining if there are any potential "close" points on the two surfaces that might intersect in the next time step.
2) Applying the penalty on them

Does that make sense?

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I'm not sure how this is incorporated into FEM framework. What you can do in FEniCS is to compute cell integrals, exterior/interior facet (facet = mesh entity of codimension 1) integrals and newly point loads (Dirac measures). But I'm not sure whether the last one is possible only at mesh vertices or at arbitrary points.