Stress tensor and partial derivatives of a force field

[Vectronix]

If F = F_xi + F_yj +F_zk is a force field, do the following derivatives have physical significance and are they related to the components of the stress tensor? I notice they have the same dimensions as stress.​

∂²F_x / ∂x²

∂²F_x / ∂y²

∂²F_x / ∂z²

∂²F_x / ∂z ∂y

∂²F_x / ∂y ∂z

∂²F_x / ∂z ∂x

∂²F_x / ∂x ∂z

∂²F_x / ∂y ∂x

∂²F_x / ∂x ∂y

The same partial derivatives of F_y and F_z

 

[Orodruin]

They have a physical significance in that they tell you something about how the force field changes. They have a priori nothing to do with the stress tensor. That two quantities have the same physical dimension does not imply that they have to be related.