Comparing FEA vs beam theory in bones: von mises vs. max. principal

[cbrassey]

Hi, I'm running some FEA models of long bones in Abaqus.

I've extracted the cross-sectional properties at midshaft, and I've calculated what the predicted bending stress would be according to Euler beam theory applying the same bending load as FEA.

When I extract stress values at midshaft from my FEA models, I get values ~20% higher for von mises, and ~30% for max. principal than predicted by beam theory.

I understand that Euler Bernoulli ignores the effects of shear, which could be quite significant, as these bones have a fairly low l/d.

My question is: is it typical for Von Mises stress to be lower than Max. Principal stress?

And wouldn't we predict Max. Principal Stress to be closer to the values predicted by beam theory than Von Mises?

Appreciate the help
Cbrassey

 

[JoshPlumSE]

When you say "mid-shaft" due you mean the stress at the middle of the cross section? Or, do you mean the stress at the mid span of the 'beam'?

One important thing to realize is that shear deformation will likely be low due to your l/d ratio. However, the shear stress may still be significant.... especially if this beam / bone is experiencing some torsional loading.

Lastly, the FEM model could be showing you some "warping" of the cross section that simple beam theory would not show.

 

[cbrassey]

Sorry, by mid-shaft I mean 'at 50% of the length of the beam'

Yes, I would expect there to be significant shearing. I'm not surprised the FEA values are higher than the simple beam predictions. I'm just unsure why von mises stress is closer to the predictions than max. principal stress.

Cheers

 

[JoshPlumSE]

Different failure criteria are used for different failure modes. In particular, Von Mises is very good when you are looking at yield stress as your failure mechanism. It's directionless, so it doesn't tell you much about how it fails other than some form of material yielding. I would think that if you combined the shear stresses from simple beam theory with the flexural stresses from simple beam theory then you would get fairly close to the Von Mises value given by your FEM analysis.

Also, if you're trying to validate your model I wouldn't look at just a single point. Instead, I'd look at the variation of stress along the length of the member. If your maximum and minimum values occur at the right locations, then that may validate the general model behavior even if in some locations your hand calculations are off by as much as 20%.... Remember FEM does tend to show localized stress risers that may be unrealistic or which are usually ignored for hand calcs.