Which is the best criterion to analyse bone?

[oguila]

Hello all!

Bone is an anisotropic material and it is considered to be brittle. However, it is modeled in most times as isotropic, as the anisotropic properties are not clear. Many times we analyse bone not to asses the simple risk of fracture, but to identify areas under high microstrains caused by repeated loads, which may lead to bone resorption.
Von Mises criterion has been used, but as bone react completely different under tension and compression, this criterion is no longer recommended. Mohr-Coulomb seems appropriate, but Ansys (14) does not have this tool... What criterion would you recommend? Principal 1?

Thanks!

 

[IceBreakerSours]

Check Doblare's review paper on bone.

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[oguila]

Thank you, IceBreakerSours! I do know the paper of Doblaré and coworkers (

http://www.ncbi.nlm.nih.gov/pubmed/14515768).

The issue is: as it is a review, they were not able to affirm which is the most suitable criterion. When the bone is assumed to be isotropic, the article suggests the Mohr-Coulomb criterion, which is not available in Ansys. As an alternative, I was wondering using the principal 1 criterion and identify the compressive and tensile maximum stresses (+ for tensile ; - for compressive). I have found that Mohr-Coulomb package is sold for Ansys, but I don´t know where or from whom.

thanks again

 

[IceBreakerSours]

I am not sure. However, the answer depends on the answers to several questions:

What kind of analysis are you performing? Static, quasi-static, implicit dynamic or explicit? What kind of material model are you assuming? Linear elastic? Hyperelastic? Hyperviscoelastic? Poroelastic? Is plasticity incorporated at all?

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[oguila]

In a simple way, I am studying the effects of a titanium device placed into bone. The Ti device is subjected to static loads. There are rough contact elements between bone and the device. The analysis is non-linear, and the the materials were set to be linear elastic. No plasticity was incorporated. The bone was modeled in a very simple manner: homogenous, isotropic, with a homogenous cortical layer over the cancellous bone. External geometry was acquired via computed tomography. Cortical bone was set to present a elastic modulus 10x bigger than cancellous. Poison coefficient was the same...

 

[IceBreakerSours]

In that case, I don't see a real need to be concerned with which failure criterion to pick. von Mises stress is a measure often used in literature.

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[oguila]

At first, I was wondering using SEQV due to the model´s assumptions. However, when I act as a journal reviewer, I always ask authors to avoid using VM analysis in bone....So I am not comfortable to use VM, even when it is not a problem.

The mech. engineer who helps me will define the Mohr´s circle and we will be able to apply this criterion.

Thanks again

 

[IceBreakerSours]

Sure. I forgot to mention another point: Bone may be considered as a fibrous composite. There may be a composites failure theory which may suit bone. Firehole Composites have a nice blog discussing various failure criteria for composites. Talk to them. If you find something interesting, please leave a note here.

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[oguila]

The Mechanical Engineer who assists me merged the results of S1,S2,S3 and shear stresses to incorporate some failure criteria (including Mohr-Coulomb, Talmax, etc...) in the Ansys (Classical) Element Table.


/post,1
cmsel,s,mm3
cmsel,a,mm4
aslv,s
lsla,s
ksll,s
eslv,s,1
nsle,s,1

St=135 !tensile strength of the material being analysed (MPa)
Sc=205 !compressive strength of the material being analysed (MPa)

SABS,1 !SABS,x (x=1 absolute value; x=0 algebric value)
ETABLE, ,S,1 !1st principal stress
ETABLE, ,S,2 !2nd principal stress
ETABLE, ,S,3 !3rd principal stress
SADD,TalMax,S1,S3,.5,-.5,, !creates element table for Talmax (TalMax)(TalMax=S3-S1)
SADD,C,S1,S3,.5,.5,, !creates element table for normal (C)(C=(S3+S1)/2)
SABS,1 !SABS,x (x=1 absolute value; x=0 algebric value)
SADD,Seq,S1,S3,1,-St/Sc,, !creates element table for equivalent stress (Seq) (Seq=S1-St/Sc*S3)
SADD,IU,Seq,,1/St,,, !creates element table for Mohr-Coulomb (IU) (IU=Seq/St)


!SigmaEq=(S1-St/Sc*S3)
!S1> 1st principal stress (maximum)
!S3> 3rd principal stress (minimum)
!St> tensile strength
!Sc> compressive strength

 

[oguila]

Correction: For the above command, the module must be off (SABS,0)!

 

[delta0]

Brittle materials are best modelled using Maximum Normal Principal Stress criterion. This is typically based on Rankine.

 

[IceBreakerSours]

I am not familiar with ANSYS; is this a user-defined failure criteria? If so, what's the idea behind this failure criteria?

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