The discussion revolves around the differences between the shear stress components τxy and τyx in the context of the Cauchy stress tensor. Participants explore the definitions, implications, and applications of these components, as well as the broader context of stress analysis in materials, particularly in relation to cubic structures.
Participants exhibit disagreement regarding the interpretation of τxy and τyx, with some asserting they are the same and others questioning this. The discussion about the symmetry of the stress tensor also remains unresolved, with varying levels of understanding and acceptance among participants.
Participants express confusion over the definitions and implications of shear stress components, as well as the assumptions underlying the analysis of stress in cubic structures. The discussion reflects a need for clarity on the derivation of the symmetry of the stress tensor and its practical implications.
##\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.chetzread said:
ok , one more question , why we need to consider the forces acting on 3 surfaces only ? There are 6 face for cubic , right ?Chestermiller said:
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.chetzread said:
so , in this case , the author in wikipedia only consider 3 surface ? Which is accepatble , too ?Chestermiller said:
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 ...?Chestermiller said:
I don't know. I always get the two confused. And it doesn't matter anyway because the stress tensor is symmetric.chetzread said:
continue from post #6 ,Chestermiller said:
They usually "prove" this using a balance of moments.chetzread said:
It looks to me like the guy in wiki is correct for the three surfaces he considered.chetzread said:
If we consider 6 surface, then it's wrong?Chestermiller said:
What do you mean? I m getting more confused now...Chestermiller said:
Look up in the literature or on Google how it is shown that the stress tensor is symmetric.chetzread said:
OK, is my idea in post #6 correct?Chestermiller said:
It really doesn't matter if the stress tensor is symmetric.chetzread said:
So, both my post and your post could be correct?Chestermiller said:
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.chetzread said:
Do you have any notes or online notes that explain further on this part? I have tried to search online , but no avail..Chestermiller said:
