Stress tensor and partial derivatives of a force field

Vectronix · Aug 3, 2017

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 · Aug 3, 2017

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.

Stress tensor and partial derivatives of a force field

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