Pressure-Inflation Boundary Condition Query

[chrismi]

Dear Professors,

I'm having difficulty determining how to apply the desired boundary conditions for the problem I'm trying to solve. I wasn't sure where exactly to post this query, so I chose "General Questions".

I am modelling the in vivo deformation of the cornea (eye tissue), which is essentially equivalent to a classical bulge-inflation test. I've provided a few figures for illustrative purposes. I'm applying the pressure using surface elements (highlighted red) with a follower load, applied to the interior surface.

However, the boundary conditions at the periphery are not quite as trivial as defining the loading. I want to enforce that the tangent to the central plane (red dotted line) where it meets the periphery (purple marker) is always orthogonal to the periphery (blue line), which would provide some rotational freedom. The provided diagram is for the 2D section, as it's difficult to visualise the issue properly in 3D.
 
I am using version 8.4 of FEAP, if that is of significance.

I look forward to hearing back from you!

[FEAP_Admin]

What else is allowed to occur at the boundary edge?  It appears that there is free rotation.  Is the purple point fixed or can it translate?  Can the edge warp? etc.?  Also are you trying to model a particular experiment? if so can you describe the actual experiment?

[chrismi]

Sorry, my initial post wasn't very clear. I'm trying to replicate the in vivo deformation of the cornea when subjected to intraocular pressure within the eye. The boundary conditions are supposed to reflect the action of the surrounding tissues (iris, sclera), which are relatively soft and allow for the rotational freedom of the cornea under physiological deformation.

Therefore, the purple point (which in 3D represents a line around the periphery) should be fixed in space, and orthogonality conditions should be preserved with respect to the deformed mid-section of the cornea. There are no other restrictions.

Thank you for response, and taking the time to answer my questions.

[Prof. S. Govindjee]

I would suggest that you construct a model of the limbus around your cornea model using elastic elements with the appropriate stiffness but without all the geometric detail, and then fix the outer part of your limbus model.  The support for the cornea seems like an elastic foundation and it is probably better to just model a bit of the foundation so as to not to over or under constrain your cornea model.  This will be a lot easier than try to enforce a complex boundary condition and it will probably be closer to the physical reality.

[chrismi]

Dear  Prof. S. Govindjee,

Thank you for your response.

That is indeed something I've considered and will likely attempt as a last-case scenario. The problem is that the meshes/geometries that I'm using are patient-specific and have been derived from corneal topography images, so generating additional elements to represent the surrounding tissues beyond the limbus would mean adding a degree of uncertainty to an already well-established geometry. Also, the sclera is a complicated tissue in its own right, and if included, I'd have to properly account for how it integrates/anchors with the cornea at the limbus.

The free rotation boundary conditions I described have been successfully implemented in my colleague's purpose-built in-house FE software, and multiple studies have demonstrated its suitability in replicating the in vivo deformation of the cornea. So I would very much like to employ the same boundary conditions in FEAP, using the material model I've already implemented using the user element functionality (a previous model I developed that I've repurposed to describe the cornea), to form an effective comparison with my group's prior work.

With that in mind, would it be possible to implement these boundary conditions in FEAP? And if so, could you please point me in the right direction of how to do so? I would greatly appreciate any help you could provide me.

[Prof. R.L. Taylor]

It is not clear what the shape of the patient specific meshes looks like.  Are they irregular or some smooth surface?

Are there equations for the 3-d boundary conditions to be imposed?  Can you describe exactly what your colleagues implementation is?  The boundary conditions is nonlinear and most likely in feap can be implemented as a user element using either Lagrange multiplier constraints or aa penalty approach.