Question about units, scaling, and nodal reaction forces

[cjadelis]

Hi Everyone,

I was hoping that someone could sanity check me here in regards to how I am defining a model I am working with. I have a model of an index finger with extensor hood, which is very similar to the example model (mi29.feb?) The materials for the various regions of the extensor hood are defined in MPa (eg. E = 120), the springs that are included in the model have their spring constants defined in N/mm, and the model itself uses dimensions in mm (so 1 unit in FEBio studio = 1 mm).

What I am wondering, however, is that if I run the model by applying a load in N (eg. load = -12) to any of the tendons, the model may or may not converge (especially if I proscribe rotations at the joints, the model may not converge). Additionally, when it does, I am able to read the plot file and get out nodal reaction forces, which typically are in the hundreds of N, which I believe shouldn't be the case, as the input loads were only in the range of 0-12 N. I was wondering if I need to apply a scaling factor to my inputs or to the outputs to account for my units (divide by 1000)?

Additionally, if I redefine my materials to be in Pa, (eg. E = 120e6), my results seem to become more stable, but my output forces then are scaled accordingly (12N in, gives 9e6 N out). Which doesn't make a whole lot of sense to me? Scaling the model itself may be possible to get everything in standard units of newtons, pascals, and meters, but currently it seems to break the model when I try to do that. Using existing data, I am able to get similar stress values as outputs to what should be expected, its mostly just the reaction forces that are way too high. I have a .feb that converges that I've attached (it's a .zip because the limit for .feb files is 2MB and this one is 4MB), and I was wondering if anyone could potentially provide some insight.

Let me know what you think

Best,
Chris

Finger_model_05222020.zip

[ateshian]

Hi Chris,

I downloaded your model, ran it with FEBio3 and displayed the results in PostView, and I cannot confirm everything you report:

You say that are "applying a load in N (eg. load = -12)". Looking at the nodal loads in your model, I find that they add up to 63.9 N (I multiplied each nodal load by the number of nodes on which it was applied). You say that you "get out nodal reaction forces, which typically are in the hundreds of N". However, looking at the model results, there are no nodal reaction forces (one can only have nodal reaction forces if there are prescribed nodal displacements in the model, but your model doesn't have any).

The only available reaction forces are for the rigid bodies representing the three phalanges. The peak value of the reaction force magnitude is 47 N, which would be consistent with the applied nodal loads. I also added "contact force" as a plot variable and its peak magnitude is 4 N (for the contact between the tendon and phalanges).

So I don't see any obvious concern with the units and magnitudes of your results. Would you please clarify where your finding nodal reaction forces in the hundreds of N?

Best,

Gerard

[cjadelis]

Hi Gerard,

Thank you for taking a look at the model, I really appreciate it. I think your first point helped a lot in correcting a misunderstanding that I was having in regard to nodal loads. My intention was to apply 12N across that entire set of nodes, not on each node individually. Where I was measuring reaction forces was selecting reaction forces in the plot file, and the graphing the reaction forces for the nodes at the terminal slip, which is hidden by the distal phalanx (the nodes at the very end of the extensor hood), at the central slip, which is implemented as a series of spring elements that contact the medial phalanx, and the two sets of adhesions which are the springs on either side of the finger connecting to the proximal phalanx close to the metacarpal bone. The first two are joined with the rigid bodies through rigid contact interfaces, and the set of adhesions share nodes with the proximal phalanx.

I changed the model and divided the load I wanted to apply by the number of nodes it would affect and I am getting much more reasonable results (though for some reason it may fail to converge at time 1.999 of 2), with the reaction forces reporting ~9.3N at the terminal slip for a 4.35N input at the EDC tendon (0.3107N applied on 14 nodes). I was getting hundreds of newtons before when I would integrate over the nodes at the fingertip, or at the central slip. Additionally, when I would change the material stiffness properties by multiplying each material's modulus by 10^6 I would get very high reaction forces as well, which I don't think is quite right, as I don't think the dimensions work out by just adjusting the modulus.

I've attached an updated version of what I have been working on that hopefully is a lot more reasonable. Additionally, after reading through some other posts, I believe that I am not measuring nodal reaction forces, but instead the rigid body reaction forces at those nodes? Would that report the net forces on the rigid body or just the forces at that node? The reason I ask, and I hope it is not outside the scope of this forum, is that my goal with this model is to record the forces exerted on the rigid bodies by the tendons and adhesions at their insertion sites for use in another simulation software (OpenSim). I was hoping that reaction forces would be the output I am looking for, but from the outputs I am observing, if I have multiple insertions on a given bone, I may not be getting just a single insertion's or adhesion's contribution. Is there a different output that I should be looking for instead? Let me know what you think, and if the above makes sense or is correct.

Best,
Chris

test_RU_config_EDC.zip

[ateshian]

Hi Chris,

I hadn't noticed originally that you had discrete elements (springs) in your model, sorry about that. However, when you request nodal reaction forces ("Rx;Ry;Rz" in the log file) for the nodes that are connected to these springs, the log file actually returns the reaction force for the rigid body to which each node is connected (so this is a duplication of the plot variable "reaction forces").

In your model, there are multiple forces acting on each rigid body (the metacarpal and phalanges):

- Contact forces (with the tendon), available via the "contact force" plot variable
- Rigid connector forces (e.g., revolute joints), available via the "RCFx;RCFy;RCFz" log variables (but not for the "generic rigid joint" used in your model)
- Discrete element forces, not directly available for output at this time
- Ground reaction forces (when the rigid body is fixed to the ground), available via the "rigid force" plot variable. (In your model, only the metacarpal produces a non-zero rigid force.)

The "reaction force" plot variable is a bit of a strange beast: It is the sum of the contact and discrete element forces, "reaction force" = "contact force" + "discrete element forces". Basically, it calculates the forces acting on the discretized surface and nodes of the rigid body. So, in this way, it is possible to extract "discrete element forces" = "reaction force" - "contact force", since the latter two are available as plot variables. For a rigid body fixed to the ground, "reaction force" will produce values of zero if the rigid body uses fixed bc's. Instead, one should use prescribed bc's to be zero in order to get a non-zero "reaction force" for that rigid body.

In a quasi-static analysis (which is the analysis in your model), the sum of all forces acting on the rigid body must be equal to zero. This means that "reaction force" + "rigid connector forces" + "rigid force" = 0. You can verify this result in your model (with some cutting and pasting of plot and log variables to a spreadsheet) using the attached model file (test_RU_config_EDC_rj.feb.zip). This file is a modification of your model which uses "rigid revolute joint" instead of "generic rigid joint" to allow log output of the rigid connector reaction forces; it also prescribes the bc's of the metacarpal to be zero, instead of fixing them; and it uses three contact interfaces, one for each of the metacarpal, proximal phalanx and middle phalanx, to separate the "contact force" values for each bone. It converges will to the final time point of t=2.

Let me know if you require further clarifications.

Best,

Gerard