# Volumetric strain

by johnboy14
Tags: strain, volumetric
 Sci Advisor P: 5,095 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 $$\nu$$?