Fluid mechanics cauchy's stress tensor

Question

Is cauchy's stress tensor symmetric always?Does this symmetricity hold in accelerating and non-zero cross velocity gradient flow field?

Have a look here : http://homepages.engineering.auckland.ac.nz/~pkel015/SolidMechanicsBooks/Part_III/Chapter_3_Stress_Mass_Momentum/Stress_Balance_Principles_03_The_Cauchy_Stress_Tensor.pdf — Solar Mike, Mar 20 '18 at 18:10

score 1 · Answer 1 · answered Mar 21 '18 at 06:30

1

The symmetric property of stress tensor is generally proved through Moment of momentum on a fluid element

So it holds as long as momentum conservation and moment equilibrium are satisfied for that element.

answered Mar 21 '18 at 06:30

mustang

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score 1 · Answer 2 · answered Mar 23 '18 at 21:03

As @mustang says, the symmetry of the Cauchy stress is a direct consequence of the conservation of angular momentum. However, angular momentum is not conserved in a non-inertial frame and one has to use an inertial frame of reference to take advantage of stress symmetry.

Fluid mechanics cauchy's stress tensor

2 Answers2