# Volumetric strain

1. Dec 3, 2006

### johnboy14

1. The problem statement, all variables and given/known data

How do I solve the following block to find the volumetric strain. Its question 3 on the link

http://img201.imageshack.us/my.php?image=file0001pf0.jpg

I know that volumetric strain is equal to change in volume EV/ origninal volume(V)

Is Ev = Ex + Ey + Ev equal to volumetric strain.

I was told that the volumetric strain should be about 6.8 x 10^-4

Any help would be appreciated people.

2. Dec 3, 2006

### FredGarvin

I am used to seeing volume dilation as the sum of the principal strains.

$$D = [\epsilon_1 + \epsilon_2 + \epsilon_3] = J_1$$ where $$J_1$$ is the first strain invariant.

I would tackle the problem that way. Calculate the principal strains and add them together.

EDIT: After looking at the problem, it is in a state of zero shear. Therefore $$\sigma_x$$, $$\sigma_y$$ and $$\sigma_z$$ are going to be the principal stresses. So, if you calculate the strains from the principal stresses you will be calculating the principal strains. Things should be pretty straight forward. I ended up calculating $$6.5 x 10^{-4}$$

Do you know the 3 dimensional stress-strain relations that involve E and $$\nu$$?

Last edited: Dec 3, 2006
3. Dec 4, 2006

yes I do

E = 200x10^9
v = 0.3

4. Dec 4, 2006

### FredGarvin

Those are constants, not the relations themselves. I meant the entire relations, i.e. equations.

Hint: There are three equations you're looking for and each equation will have one strain element and all three stress elements.

Last edited: Dec 4, 2006