I've come across this phenomenon several times and never found any real reason for this.

When I consider a cylindrical object like a rod, I need to calculate several things. One of those is the stress tensor in cylindrical coordinates represented by $r$, $\theta$, and $z$ directions.

Now, in many books and in my lecture notes there's always this one line that says:

$$ \frac{\partial\bullet}{\partial\theta}=0$$

I know that when compressing a steel rod (assuming there is little to no friction at the contact points) the steel rod should get compressed in the $z$-direction and expand in the radial direction. Why is there no stress in the circumferential direction?

I've looked in many places and I hope that I didn't accidentally miss the other SE question with respect to this specific topic.