According to the text books a material with a Poisson ratio of 0.5 does not undergo a volume change on compression or extension. This means that the ratio of strains in the z and y (compared to x the force direction) is 0.5. So a unit cube with a x strain of 0.2, the y and x components would be -0.1. I take this to mean that the final dimensions of the cube would be 0.9, 0.9, and 1.2 (I am probably wrong here?) and so the volume is now 0.9 x 0.9 x 1.2 = 0.972 i.e a volume change.
help a struggling chemist (I have to teach some simple mechanics on a course on plastics so I had better understand it myself first!)
It’s only approximate. Look at equation II©(2) on this page:
A different explanation.
The proper formula for the volume is:
V = (1 + e)(1 - ve)(1 - ve) = 1 + e - 2ve - 2ve[sup]2[/sup] + v[sup]2[/sup]e[sup]2[/sup] + v[sup]2[/sup]e[sup]3[/sup]
where
V = volume,
e = strain, and
v = Poisson’s ratio.
If e is small, the terms 2ve[sup]2[/sup], v[sup]2[/sup]e[sup]2[/sup] and v[sup]2[/sup]e[sup]3[/sup] are negligible, giving:
delta V = e (1 - 2v)
So according to that equation, if v = 0.5, delta V = 0.
However, the value of e that you’ve used is large, and so the equation doesn’t work.
thanks people. To think of the number of hours wasted on that one. Stupid text books - never trust them again :smack: