##\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:
A Cauchy stress tensor is a mathematical representation of the stress state at a specific point in a continuous medium, such as a solid or fluid. It is a second-order tensor that describes the magnitude and direction of the stress acting on a given surface at that point.
A Cauchy stress tensor is calculated by taking the derivative of the force vector with respect to the area vector on an infinitesimal surface element in the material. This is represented mathematically as the gradient of the stress tensor.
A Cauchy stress tensor provides information about the internal forces and stresses within a material, including both normal and shear stresses. It can also provide insight into the deformation and behavior of the material under different loading conditions.
The Cauchy stress tensor is a fundamental concept in mechanics, as it allows for the analysis and prediction of the behavior of continuous materials under different types of loading. It is used in numerous fields, including solid mechanics, fluid mechanics, and structural engineering.
The Cauchy stress tensor has numerous applications in various fields, including stress analysis of structures, design of mechanical components, prediction of material failure, and simulation of fluid flow. It is also used in the development of mathematical models and simulations in materials science and engineering.
