# Homework Help: Cauchy stress tensor

1. Sep 6, 2016

1. The problem statement, all variables and given/known data
https://en.wikipedia.org/wiki/Cauchy_stress_tensor

I dont understand the difference between τxy . τyx , τxz , τzx , τyz , τzy ..What did they mean ?

2. Relevant equations

3. The attempt at a solution
taking τxy and τyx as example , what are the difference between them ? They are the same , right ? they mean the shear force shear the xy plane , right ?

2. Sep 6, 2016

### Staff: Mentor

$\tau_{xy}$ represents the shear stress in the x direction on a plane of constant y. $\tau_{yx}$ represents the shear stress in the y direction on a plane of constant x.

3. Sep 6, 2016

ok , one more question , why we need to consider the forces acting on 3 surfaces only ? There are 6 face for cubic , right ?

4. Sep 6, 2016

### Staff: Mentor

You can get the forces on all 6 faces of the cube using the Cauchy stress relationship, and taking into account the possibility that the stress tensor may be varying with spatial location.

5. Sep 6, 2016

so , in this case , the author in wikipedia only consider 3 surface ? Which is accepatble , too ?

6. Sep 6, 2016

i think you mean $\tau_{yx}$ represents the shear stress in the x direction on a plane of constant y and vice versa ??? because the force σyx (τyx) is in the x direction at constant y ......???

7. Sep 6, 2016

### Staff: Mentor

I don't know. I always get the two confused. And it doesn't matter anyway because the stress tensor is symmetric.

8. Sep 6, 2016

continue from post #6 ,
because the force σyx (τyx) is in the x direction at constant y ......???

9. Sep 6, 2016

### Staff: Mentor

They usually "prove" this using a balance of moments.

10. Sep 6, 2016

### Staff: Mentor

It looks to me like the guy in wiki is correct for the three surfaces he considered.

11. Sep 6, 2016

If we consider 6 surface, then it's wrong?

12. Sep 6, 2016

What do you mean? I m getting more confused now.....

13. Sep 6, 2016

### Staff: Mentor

Look up in the literature or on Google how it is shown that the stress tensor is symmetric.

Last edited: Sep 6, 2016
14. Sep 6, 2016

OK, is my idea in post #6 correct?

15. Sep 6, 2016

### Staff: Mentor

It really doesn't matter if the stress tensor is symmetric.

16. Sep 6, 2016

So, both my post and your post could be correct?

17. Sep 7, 2016

Sorry, I have another notes here... I couldn't understand why the (tau)_xy could be = (tau)_yx? Why should they be the same?

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18. Sep 7, 2016

### Staff: Mentor

I recommended references that contain the same kind of derivation that is in virtually every textbook. And I already alluded to a balance of moments. The rest is up to you to work out.

19. Sep 7, 2016