How Do You Calculate the Winkler Foundation Modulus for Bone?

[cabellos6]

Winkler foundation modulus...?

I need to find the Winkler foundation modulus of bone. Does anyone know this or know of a means to calculate this?

Thankyou.

 

[Danger]

I can't help you on this at all, but I'm wondering if you might have more luck in the Medical Science forum. It sounds like a bio-engineering problem to me.

 

[Pyrrhus]

Bone? why bone? hehe. Winkler method is familiar for me only for designing slab on grade foundations, so i know a couple of values for different type of soils, but bone? that's new to me, hehe.

 

[NoTime]

That was my first guess as well Danger.
However, Winkler Foundation seems to be an engineering thing involving stress, elastic deformation and buckling in materials.

Applied to bone there are a lot of subscription journal abstracts, but I couldn't find any free articles available on the net.

Looks like a trip to the library, unless you have online journal subscriptions.

 

[Danger]

There's another approach, which might not work in this case. Things are a bit casual in Canada. I used to just stroll down into the bowels of the largest local hospital to whatever lab interested me and chat with whoever was working there. It's amazing what a free education you can get hanging out with people that no-one else wants to associate with.

 

[FredGarvin]

In cases like this, experimental techniques should probably be used. You'll have to get samples to a testing facility to measure it. That is, unless you happen to run across someone who knows this. Bio-med engineers are your best bet.

 

[cabellos6]

Just had a browse through some journals and came across this http://www3.interscience.wiley.com/cgi-bin/fulltext/109927764/PDFSTART"

On page 4 it talks about the value of K. I am not sure whether this 5.8 is a general approximated value for bone?

 

[FredGarvin]

I can't see the article. However, K is usually a variable that represents a force per unit length, not area, i.e. a spring constant. I'm not so sure that would be applicable if that were the case.

 

[Mapes]

Take another look at your Winkler foundation literature and check whether it uses the modulus E (the Young's modulus), $\mu$ (the shear modulus), or K (the bulk modulus).

Then search for the Young's modulus E and Poisson's ratio $\nu$ of bone. There will be many different values, especially for trabecular (meshlike) vs. cortical (solid) bone, so make sure you've found the type of bone that you're modeling.

The moduli are coupled by the following relationships:

$$\mu=\frac{E}{2(1+\nu)}$$
$$K=\frac{E}{3(1-2\nu)}$$

Use the correct modulus as input for your Winkler foundation model.

 

[cabellos6]

Thanks. Could i just ask is there any particular book/website you found these relationships from?

 

[Mapes]

Sure, look at Wikipedia's entry for "elastic moduli." It's easy to get confused with all the variables, but there are only two independent variables for linear elastic isotropic materials. You just need to connect the variables in the elasticity literature with the experimental data in the biomedical literature. Good luck.

 

[FredGarvin]

Take another look at your Winkler foundation literature and check whether it uses the modulus E (the Young's modulus), $\mu$ (the shear modulus), or K (the bulk modulus).

Then search for the Young's modulus E and Poisson's ratio $\nu$ of bone. There will be many different values, especially for trabecular (meshlike) vs. cortical (solid) bone, so make sure you've found the type of bone that you're modeling.

The moduli are coupled by the following relationships:

$$\mu=\frac{E}{2(1+\nu)}$$
$$K=\frac{E}{3(1-2\nu)}$$

Use the correct modulus as input for your Winkler foundation model.

Those relations assume a linear, isotropic material. I am not so sure that applies in the case of bone which can be porous and contain voids in some cases.

 

[cabellos6]

I just found on another forum the winkler modulus can be estimated by the following expression:

k = E*(1/B+1/L+1/h)

where E is the youngs modulus of foundation, B is width of strip, L is the length of strip and h is the limit depth (of soil in this case)

How could i estimate my limit depth h of my bone surface?

 

[sfbm]

I just found on another forum the winkler modulus can be estimated by the following expression:

k = E*(1/B+1/L+1/h)

where E is the youngs modulus of foundation, B is width of strip, L is the length of strip and h is the limit depth (of soil in this case)

How could i estimate my limit depth h of my bone surface?

can you please quote an reference for this value of "K"

 

[sfbm]

I just found on another forum the winkler modulus can be estimated by the following expression:

k = E*(1/B+1/L+1/h)

where E is the youngs modulus of foundation, B is width of strip, L is the length of strip and h is the limit depth (of soil in this case)

How could i estimate my limit depth h of my bone surface?

Please tell me the refernce for this equation