So I'm just learning about Stress Tensors and have had an on going confusion and I'm wondering if the cube diagrams may to be blame. Usually when a stress tensor is introduced they show a cube and explain that the corresponding 9 components of the stress tensor represent the the 9 strains on the 3 faces of the cube that one can see.
But if we are considering the possible forces on the faces of a cube, I would want there to be 18 components, that is, 3 components for each of the 6 faces. So I'm wondering if the cube diagram is really just an over simplification to try and give some intuition to students who won't delve into the mathematical details.
I'm wondering this because I finally came across direct reference to Cauchy's stress theorem which explains how the stress across any plane through the point in question can be determined by knowing the stresses on the 3 perpendicular planes. This seems like it would provide the 9 components.
So is my thinking correct? Is the cube not really an accurate portrayal of the underling mathematics?