Hi Matt,

It is difficult to give a clear answer without some more information on how you 
want to compute with fibers and where the material model for the fibers is 
coming from.

If you have a way to compute the fourth-order tensor directly then an approach 
like the one in the linked paper works. A good alternative is to compute a 
vector field which represents the anisotropic property - a good description of 
this for cardiac simulations is given in Pasquale's paper from early this year:

https://arxiv.org/pdf/2101.10960.pdf

that process (similar to what we do at UNC) involves computing a fiber field as 
a finite element field, so you don't necessarily need to store quadrature data 
- you can just compute values that you need cell-by-cell.

Best,
David
________________________________
From: dealii@googlegroups.com <dealii@googlegroups.com> on behalf of Matthew 
Rich <mjric...@gmail.com>
Sent: Thursday, September 30, 2021 9:49 PM
To: deal.II User Group <dealii@googlegroups.com>
Subject: [deal.II] Implementing a fiber reinforcement in a biphasic model

Hi all,

I am trying to add some anisotropy to my model via fibers. These fibers would 
only be active in tension and have different orientations depending on spatial 
location in the model. My plan of attack was to simply store and extra value at 
the quadrature points that had a direction representing the fiber and update 
directions after each time step. (is this a good way to go about doing that). I 
see a lot of papers doing fiber models in ABAQUS or COMSOL, but I never see any 
details on how to do it so I am guessing it is trivial.

Then I stumbled upon https://doi.org/10.1016/j.compstruc.2020.106334 which uses 
dealii to implement a fiber model that has two grids and some sort of junction 
between the grid representing the bulk material and one presenting the fiber. 
The formulation seemed way more involved than what I was going to try.

Am I making a gross simplification in my proposed approach.

Matt




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