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

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SUMMARY

This discussion focuses on the relationship between longitudinal and transverse strains in a 3D rectangular object, specifically addressing why Poisson's ratio indicates that the transverse strain in one direction (∆a/a) equals the transverse strain in another direction (∆b/b). The conversation highlights that when a rectangular bar is subjected to stretching in the longitudinal direction (L), the resulting transverse strains in the width (A) and height (B) are equal due to the material's homogeneous stress state. This equality is a fundamental property of isotropic materials, governed by Poisson's ratio.

PREREQUISITES
  • Understanding of Poisson's ratio
  • Basic knowledge of strain and stress concepts
  • Familiarity with 3D geometry in material science
  • Knowledge of homogeneous stress states in materials
NEXT STEPS
  • Study the derivation of Poisson's ratio in isotropic materials
  • Learn about the implications of homogeneous stress in material deformation
  • Explore the mathematical relationships between longitudinal and transverse strains
  • Investigate applications of Poisson's ratio in engineering materials
USEFUL FOR

This discussion is beneficial for materials scientists, mechanical engineers, and students studying material mechanics, particularly those interested in the behavior of materials under stress and strain conditions.

Kabo111
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In poisson's ratio

If we are stretching a a 3d rectangle
L is height
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.
 
Physics news on Phys.org
The bar of rectangular cross section is in a state of homogeneous stress. What is the stress in the “a” direction? What is the stress in the “b” direction?
 

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