# Winkler foundation modulus ?

1. Feb 26, 2008

### 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.

2. Feb 26, 2008

### 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.

3. Feb 26, 2008

### 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.

4. Feb 26, 2008

### 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.

5. Feb 26, 2008

### 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.

6. Feb 26, 2008

### 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.

7. Feb 27, 2008

### cabellos6

Last edited by a moderator: Apr 23, 2017
8. Feb 27, 2008

### 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.

9. Feb 27, 2008

### 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.

10. Feb 27, 2008

### cabellos6

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

11. Feb 27, 2008

### 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.

12. Feb 27, 2008

### FredGarvin

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.

13. Feb 27, 2008

### 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?

14. Jul 5, 2010

### sfbm

Re: Winkler foundation modulus....?

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

15. Jul 6, 2010

### sfbm

Re: Winkler foundation modulus....?

Please tell me the refernce for this equation