What stress tensor components mean?

[eprparadox]

Hey! I'm reading a book Intermediate Physics for Medicine and Biology

In it, there is a section that is describing shear forces and it says this as a side note:
In general, the force F across any surface is a vector. It can be resolved into a component perpendicular to the sur- face and two components parallel to the surface. One can speak of nine components of stress: Sxx,Sxy,Sxz,Syx,Syy,Syz,Szx,Szy,Szz. The first subscript denotes the direction of the force and the second denotes the normal to the surface across which the force acts. Components Sxx,Syy and Szz are normal stresses; the others are shear stresses. It can be shown that Sxy = Syx, and so forth.

I'm having a hard time understanding this:
...and the second denotes the normal to the surface across which the force acts.

I'm not understanding this second subscript. If we take Sxx for example, then we're talking about the x-direction of the force and what does that second x mean? I'm confused by this.

Thanks for any insight provided.

 

[Andy Resnick]

Personally, I refer to this mental image:

https://upload.wikimedia.org/wikipe...px-Components_stress_tensor_cartesian.svg.png

The diagonal components (Sxx, Syy, Szz) can be thought of as a pressure or 'normal force', while the off-diagonal components refer to shear or 'in-plane forces'.

 

[eprparadox]

Awesome, i should have checked wikipedia first. This image makes way more sense than the written description

Thanks a lot @Andy Resnick

 

[Chestermiller]

I'm having a hard time understanding this:
...and the second denotes the normal to the surface across which the force acts.

I'm not understanding this second subscript. If we take Sxx for example, then we're talking about the x-direction of the force and what does that second x mean? I'm confused by this.

The 2nd subscript means "on a plane perpendicular to the x axis." So Sxx is the force per unit area acting in the x direction on a plane perpendicular to the x axis.

Chet