Pure Shear Questionthanks for your help

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    Pure Shear
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SUMMARY

The discussion centers on proving that a state of pure shear results in no volume change during linear elastic deformation. The participant demonstrates a solid understanding of shear stresses and strains but struggles with the proof. Key concepts include the relationship between volume deformation and principal stresses, specifically in the context of Young's Modulus and standard strain and stress equations. The participant seeks guidance on expressing volume deformation in terms of principal stresses under pure shear conditions.

PREREQUISITES
  • Understanding of shear stresses and strains
  • Familiarity with linear elastic deformation principles
  • Knowledge of Young's Modulus and its applications
  • Proficiency in basic strain and stress equations
NEXT STEPS
  • Research the relationship between principal stresses and volume deformation in materials
  • Study the derivation of the equations governing linear elastic deformation
  • Explore examples of pure shear states in engineering materials
  • Learn about the implications of shear stress on material properties
USEFUL FOR

Students in mechanical engineering, materials science, and structural engineering who are studying the principles of elasticity and deformation in materials.

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Homework Statement


Hey everyone. I was practicing some problems, and I came across one that seems pretty simple, yet I am having difficulty proving the answer. The question asks us to show that a state of pure shear causes no volume change in linear elastic deformation. I have a very good understanding on shear stresses and strains, however, this problem seems harder then it actually is. If someone could point me in the right direction I would appreciate it greatly!


Homework Equations


Strain Eq, Stress Eq, Young's Modulus (standard elementary equations)


The Attempt at a Solution



I have literally spent hours reading my book and working out problems, such as these. I seem to understand all of the formulas, however, I am having trouble proving the statement.
 
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What is the expression for volume deformation, i.e. how does it relate with the principal stresses? What are the values of these stresses for the pure shear state?
 

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