FEA vs beam theory in bones - Max. Principal and Von Mises

[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

 

[Twoballcane]

Well first is this for school?

Tobalcane
"If you avoid failure, you also avoid success."
“Luck is where preparation meets opportunity”

 

[rb1957]

von Mises considers all three principal stresses; look intothe formula for vM (it's everywhere, including wiki).

your FE, presumably solid elements, includes a whole bunch of things that your My/I calc doesn't, shear delection being one. if you want to validate your modelling, i'd start with something simpler, like a beam element, which should be much closer to My/I.

 

[btrueblood]

Not sure I would trust VonMises theory for a brittle material like bone...but I'm no bioengineer, either.

 

[rb1957]

why not ? i'd've thought since it's elastic strain energy (ie not plastic, not ductile) that it'd fit brittle materials ... but then i'd stay away from brittle materials in the 1st place.

 

[IDS]

Can you post a picture of the model, a diagram of the loading, and the stress distribution across the section you are looking at?

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[btrueblood]

Rb, I was larned that brittle materials are best modelled based on a max. principal stress; later worked with/studied under a gentleman modelling shuttle tiles, he and a team of grad students developed a stochastic theory that did a fairly good job of predicting average tile loss over time, but was still based on max. principal stresses at the root. Von Mises is not elastic strain energy, it's octahedral shear stress, and best models ductile yield.

 

[btrueblood]

Uh, ok, Von Mises is called by some "maximum elastic distortional energy criterion", i.e. strain energy less the dilational (hydrostatic) component.

 

[rb1957]

my point was that vM is valid up to yield, as you note "elastic". as i said i prefer to avoid brittle materials in the 1st place, and i personally prefer max principal as my failure criteria.

 

[jhardy1]

@rb1957

"... but then i'd stay away from brittle materials in the 1st place."

The OP is talking about analysing bone - I guess god got it wrong when he made us with brittle bones - he should obviously have created us with nice ductile bones!

http://julianh72.blogspot.com

 

[dwallace1971]

Maybe we'll see that in the next design release.

"On the human scale, the laws of Newtonian Physics are non-negotiable"

 

[rb1957]

julian,

i guess i'm not god ...

 

[btrueblood]

"Avoid brittle materials" - I'd agree in general, but ceramics can be useful at high temperatures. And carbon and glass fibers are kinda handy stuff too.

As far as god and intelligent design go...why'd he/she put the amusement park so darn close to the sewer outlet?