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Does the Cauchy stress tensor under static equilibrium in a fluid HAVE to be isotropic? If so why? I would like to be pointed to rigorous mathematical resources that show this. What physical constitutive assumptions leads to this?

Chockalingam Senthilnathan
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    I found the answer in Professor Rohan Abeyaratne’s notes from MIT – Chockalingam Senthilnathan Sep 20 '22 at 20:39
  • Would you care to post the answer you've found as a self-answer here? – Daniel Hatton Sep 23 '22 at 10:51
  • It can be shown using the fact that every uni modular transformation of the reference configuration is a material symmetry group along with the principle of material frame indifference. Physically this corresponds to the constitutive assumption that the fluid response is independent of reference configuration. For viscoelastic fluids this only holds when the fluid flow has stopped (static equilibrium). This constitutive assumption also inherently means the fluid is isotropic, for anisotropic fluids such as liquid crystals it does not hold. – Chockalingam Senthilnathan Sep 25 '22 at 07:15

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