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.
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]?
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.