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poisson effect

When we have stress, say in x direction, due to poisson effect, we get strain in y and z directions.

What is the reason that associated stress does not develop due to this strain in y and z directions? Is it due to the fact that there is no restraint to this strain, something similar to when free thermal expansion does not result in stress?

Joe Kelleher's picture

Pretty much, yes. Loosely, stress is defined as the force per cross-sectional area within the material, and strain is the relative change in shape. It's perfectly possible to have one without the other, or have one in a certain direction caused by the other in a different direction. As you note, thermal expansion is a strain that does not itself either cause or result from a stress. But if you constrain the expansion you do generate a stress - or more precisely, you're constraining the total strain, so you generate an elastic strain (and hence stress) of opposite sign to the thermal strain, so that that the total strain is what you constrained it to be. Phase change strains and magnetostrictive strains are also examples of strains that don't result from stress, but again, you could get stress from attempting to constrain the formation of these strains. And if you attempted to constrain the Poisson strain in the Y and Z directions when loading in the X direction, then (and only then) you would get stress in the Y and Z directions.

Alberto Neo

I am confused. Be there no internal forces, what will hold the material together when it takes deformation? If so, why will not the intneral force produce stress?

Thanks in advance for any help.

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