# Relationship between stress and density

1. Jun 28, 2013

### MarcGyongyosi

Hi everyone,

I am curious as to whether it is possible to calculate the difference in density due to applied (mechanical) stress on an object.

E.g.: apply a controlled force of, say, 50 N on a structure, calculate the mechanical stress in the object with sigma = M/I * z and then go on from there, using some kind of relationship between stress and density to figure out how density changes throughout the object...

Looking forward to an answer, if there is one ;)

Thank you very much!

Best regards,
Marc

2. Jun 28, 2013

### sophiecentaur

Welcome to PF

The compressibility of a substance is discussed here
Everything is compressible but solids and liquids are a lot lot less compressible than gases.

3. Jun 28, 2013

### MarcGyongyosi

where?

4. Jun 28, 2013

### sophiecentaur

HAha - click on the blue "here".

5. Jun 28, 2013

### MarcGyongyosi

6. Jun 28, 2013

### SteamKing

Staff Emeritus
In a nutshell, no, there is no relationship between bending stress and the change in density of an elastic structure.

I am curious as to what prompted this question in the first place.

7. Jun 28, 2013

### MarcGyongyosi

Hi,
we are working on a problem involving stress-induced birefringence... since the dielectric constant of a substance can be put in relation with its density (Clausius-Mossotti relation) it would have been interesting to be able to link a "change in density" due to stress to a change in the dielectric constant... I guess, however, we'll have to look for another way!

But thank you very much!

8. Jun 28, 2013

### sophiecentaur

Just a thought. As the compressibility of solids is so high, would it not be more likely that a dielectric material, when deformed by a force, would assume a shape which would maintain the density, ( i.e. virtually unchanged) as it changed shape? I am not into Materials Science really but it would seem a reasonable assumption.
(I pressed the 'go' button on my first post before I was ready)

9. Jun 28, 2013

### SteamKing

Staff Emeritus
Photoelasticity also uses birefringence of materials to show the distribution of stresses within the material as it is loaded.

See: http://en.wikipedia.org/wiki/Photoelasticity

I think the C-M formula involves the density of a material, not the change in density. Are you saying that the dielectric constant a material isn't a constant?

10. Jun 28, 2013

### MarcGyongyosi

@SteamKing

given birefringence and from Maxwell's eqn. with $\mu$≈1 and εr=n2 I am trying to use the C-M formula to compute the refractive index given a volume change due to a force applied on the structure/object... I'll work on it and see if it fits the experimental data...

Marc

11. Jun 28, 2013

### Staff: Mentor

Using the 3D tensorial form of Hooke's law involving the Young's modulus and the Poisson ratio, one can calculate the change in density of a linearly elastic solid material under prescribed loading.