B Why Does Poisson's Ratio Show Equal Transverse Strain in 3D Rectangles?

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Poisson's ratio explains the relationship between longitudinal strain and transverse strain in a 3D rectangle when it is stretched. When the rectangle is elongated in the L direction, the transverse strains in both the A and B directions are equal, leading to the equation ∆a/a = ∆b/b. This equality arises from the material's homogeneous stress state, where the stress in the A direction is balanced by the stress in the B direction. Understanding this concept is crucial for analyzing material behavior under stress. The discussion emphasizes the fundamental principles of mechanics of materials.
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In poisson's ratio

If we are stretching a a 3d rectangle
L is hight
A,B are the length and width
Starching it in the L direction so that's the longitudinal strain we are making
Why does the transverse strain in the "a " side equals the strain in "b" side
So like that we can both use ∆a/a or ∆b/b
To get the transverse strain ?
I mean why is ∆a/a=∆b/b ..
Please in a simple way first , sorry for bad English or typos, I'm using my phone to submit this. Thx all.
 
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