Volumetric strain

  1. 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. jcsd
  3. FredGarvin

    FredGarvin 5,087
    Science Advisor

    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: Dec 3, 2006
  4. yes I do

    E = 200x10^9
    v = 0.3
     
  5. FredGarvin

    FredGarvin 5,087
    Science Advisor

    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
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