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Volumetric strain

  • Thread starter johnboy14
  • Start date
  • #1
22
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Homework Statement



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.
 

Answers and Replies

  • #2
FredGarvin
Science Advisor
5,066
6
I am used to seeing volume dilation as the sum of the principal strains.

[tex]D = [\epsilon_1 + \epsilon_2 + \epsilon_3] = J_1[/tex] where [tex]J_1[/tex] 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 [tex]\sigma_x[/tex], [tex]\sigma_y[/tex] and [tex]\sigma_z[/tex] 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 [tex]6.5 x 10^{-4}[/tex]

Do you know the 3 dimensional stress-strain relations that involve E and [tex]\nu[/tex]?
 
Last edited:
  • #3
22
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yes I do

E = 200x10^9
v = 0.3
 
  • #4
FredGarvin
Science Advisor
5,066
6
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:

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