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Cauchy stress tensor

  1. Sep 6, 2016 #1
    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. jcsd
  3. Sep 6, 2016 #2
    ##\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.
     
  4. Sep 6, 2016 #3
    ok , one more question , why we need to consider the forces acting on 3 surfaces only ? There are 6 face for cubic , right ?
     
  5. Sep 6, 2016 #4
    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.
     
  6. Sep 6, 2016 #5
    so , in this case , the author in wikipedia only consider 3 surface ? Which is accepatble , too ?
     
  7. Sep 6, 2016 #6
    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 ......???
     
  8. Sep 6, 2016 #7
    I don't know. I always get the two confused. And it doesn't matter anyway because the stress tensor is symmetric.
     
  9. Sep 6, 2016 #8
    continue from post #6 ,
    because the force σyx (τyx) is in the x direction at constant y ......???
     
  10. Sep 6, 2016 #9
    They usually "prove" this using a balance of moments.
     
  11. Sep 6, 2016 #10
    It looks to me like the guy in wiki is correct for the three surfaces he considered.
     
  12. Sep 6, 2016 #11
    If we consider 6 surface, then it's wrong?
     
  13. Sep 6, 2016 #12
    What do you mean? I m getting more confused now.....
     
  14. Sep 6, 2016 #13
    Look up in the literature or on Google how it is shown that the stress tensor is symmetric.
     
    Last edited: Sep 6, 2016
  15. Sep 6, 2016 #14
    OK, is my idea in post #6 correct?
     
  16. Sep 6, 2016 #15
    It really doesn't matter if the stress tensor is symmetric.
     
  17. Sep 6, 2016 #16
    So, both my post and your post could be correct?
     
  18. Sep 7, 2016 #17
    Sorry, I have another notes here... I couldn't understand why the (tau)_xy could be = (tau)_yx? Why should they be the same?
     

    Attached Files:

  19. Sep 7, 2016 #18
    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.
     
  20. Sep 7, 2016 #19
    Do you have any notes or online notes that explain further on this part? I have tried to search online , but no avail..
     
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