- #1

AndersF

- 27

- 4

- Homework Statement:
- According to Cauchy's stress theorem, the stress vector at some point in a continuous medium depends on the direction of the surface to which it is referred. Therefore, at the same point, there are infinitely many stress vectors, each of which corresponds to a different surface. How is it possible that the stress vector at the same point is not unique?

- Relevant Equations:
- ##\mathbf{T}^{(\mathbf{n})}=\mathbf{n} \cdot \boldsymbol{\sigma}##

According to Cauchy's stress theorem, the stress vector ##\mathbf{T}^{(\mathbf{n})}## at any point

##\mathbf{T}^{(\mathbf{n})}=\mathbf{n} \cdot \boldsymbol{\sigma}##

This means that, at the same point, infinite stress vectors are defined, each corresponding to a different orientation of the chosen surface. That is something that confuses me, because in the force fields I knew so far (gravitational, electromagnetic...) the force associated with each point was unique.

What is the reason for this behaviour in the case of fluids and continuous mediums?

*P*in a continuum medium associated with a plane with normal unit vector**n**can be expressed as a function of the stress vectors on the planes perpendicular to the coordinate axes,*i.e.,*in terms of the components ##\sigma_{ij}## of the stress tensor**σ**.##\mathbf{T}^{(\mathbf{n})}=\mathbf{n} \cdot \boldsymbol{\sigma}##

This means that, at the same point, infinite stress vectors are defined, each corresponding to a different orientation of the chosen surface. That is something that confuses me, because in the force fields I knew so far (gravitational, electromagnetic...) the force associated with each point was unique.

What is the reason for this behaviour in the case of fluids and continuous mediums?