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According to the Cauchy Postulate, the stress vector (T)^(n) remains unchanged for all surfaces passing through the point P and having the same normal vector n at P i.e., having a common tangent at P. This means that the stress vector is a function of the normal vector n only, and is not influenced by the curvature of the internal surfaces.

source: Wikipedia https://en.wikipedia.org/wiki/Cauchy_stress_tensor#Cauchy%E2%80%99s_postulate

So, traction vector or stress only exist at internal surfaces? What about the external surface of the continuum body (boundary surface)?

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    $\begingroup$ Note that we use MathJax to typeset mathematics; you can find a good tutorial here. $\endgroup$ Mar 29, 2021 at 13:36
  • $\begingroup$ Thank you Emilio for the reference $\endgroup$
    – user134613
    Mar 29, 2021 at 13:45
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    $\begingroup$ This follows from the principle of local action for the stress tensor. It only depends on the deformations at the immediate point under consideration. $\endgroup$ Mar 31, 2021 at 11:12

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It doesn't matter whether the surface is internal or external, all what matters is that a traction vector is a unit surface vector that acts on the surface of a body ( particles at the surface) and not on the interior of the body. Otherwise it would a body force vector that acts on the interior of a body (example: gravity force vector).

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