# Vector Interpretation Equivalent of Tensor Interpretation

Take the stress tensor as an example. Given a coordinate system, the state of stress is uniquely determined by the 9 components of the stress tensor. I interpret this statement as (please correct me if I am wrong):

"For a given plane with the normal $\bf{n}$, we can compute the stress vector acting on that plane if we know the stress tensor."

Now, take a stress vector acting on a particular plane as an example of a vector. Similar to the stress tensor, for a given coordinate system, that stress vector is uniquely determined by its 3 components.

My question is: What is the corresponding interpretation of this statement? More specifically, I am seeking an interpretation equivalent to that in the quote.

• Do you mean something like "For a given plane with the normal $\mathbf{n}$, we can compute the state of stress (i.e., the stress tensor) in the material if we know the traction vector."? I use "traction vector" instead of "stress vector" to avoid confusion. "Traction" is often used to describe a force vector being applied to the outside of a solid. – Chemomechanics Oct 17 '17 at 15:56
• @Chemomechanics I think it is an equivalent way of viewing the relationship between stress and force. Although stress is force/area, I think it is unnecessary to distinguish them temporally. This is similar to the relationship F=ma: can we have force as an entity by it self without acceleration? And when it comes to your use of the traction vector, it is just different from the stress vector by a minus sign because traction and stress have equal magnitude but have opposite directions since they act on opposite sides of the same plane. – A Slow Learner Oct 19 '17 at 14:24