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Pure Shear Questionthanks for your help!

1. 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!


2. Homework Equations
Strain Eq, Stress Eq, Young's Modulus (standard elementary equations)


3. 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.
 

Answers and Replies

radou
Homework Helper
3,104
6
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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