| |
| When the top of the cube is pressed down, the shaded |
| areas move out. |
Suppose we have a cubical (of course) water balloon, as shown. Each side is of length L. If you squash down on the balloon, it spreads out on the sides, because the water is essentially incompressible: The volume of water that leaves one part of the balloon simply shows up in another. The displaced volume shows up by pushing each of the 4 side faces out a little. The Left and Right faces move apart to accommodate half the volume, and the Front and Back faces move apart to accommodate the other half. For simplicity in the figure, we fixed the left, back, and bottom faces, so that only the right and the front were actually moved by this "side effect."
When the top of the cube is pressed down, the shaded areas move out.
If the top of the balloon moves down a distance, a, then the volume of water which leaves the top is aL. To accommodate this water, the front side moves out a distance, a/2, and so does the right side. In terms of the simple strain definition, when
then
In a more general form,
.
This is the extreme case of the "side effect," in which the material is not compressed at all.
In general, when single pair of forces is applied to
produce a tensile strain, such as
, two other
tensile strains are also produced, as a "side effect." The relation between the
"direct effect,"
, and the
"side effects,"
and
, is (for
isotropic materials):
 |
| Representatives materials and their Poisson's ratios. |
The constant
is called
Poisson's Ratio. It is true in general that
. However,
values from -1 to +0.5 are allowed theoretically. Typical values of Poisson's
ratio are given in the table.
Gortex, the Teflon based material used in athletic clothing is the only known material with a negative Poisson's ratio: When stretched in one direction, it expands in the other directions. (See Science Magazine, Vol.247,p630, Feb9, 1990.) For more information, see
http://silver.neep.wisc.edu/~lakes/Poisson.html
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