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I had this question while I was reading the differences between pressure and stress.

As I have read:

Pressure is the intensity of external forces acting on a point, and it always act normal to the surface.

Stress is the intensity of internal resistance force developed at a point, and it could be either normal or parallel.

Ok then, why isn't there a parallel or a shear pressure?

When I thought about an answer, I told myself, by referring to its definition, that it may be because it is acting on a point, so if there is a parallel pressure then it won't be acting on a point but instead it will be acting on a surface. Great then let us do another definition for a parallel pressure.

But then shear stress is acting on a surface and not on a point, so how come that stress is defined to be acting on a point while shear stress opposes this idea?

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  • $\begingroup$ Seems odd that you're trying to force an isomorphism. It's tempting, but pressure is always normal. Pressure is a type of stress in a solid (normal type), shear is the parallel type. They're not analagous, pressure is a subset of a type of stress in solids. You can also have shear and pressure in gases and liquids too though obv. $\endgroup$ – AER Jun 17 '20 at 23:45
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Pressure is the intensity of external forces acting on a point, and it always act normal to the surface.

Stress is the intensity of internal resistance force developed at a point, and it could be either normal or parallel.

Pressure and stress are not actually two different things. In fact, pressure is a part of the stress tensor. Specifically, it is the part of the stress tensor which is isotropic.

Because pressure is isotropic it must be purely normal and not tangential. This is related to the hairy ball theorem.

https://en.m.wikipedia.org/wiki/Hairy_ball_theorem

So while you certainly can have stresses that are directed parallel to the surface (shear stresses) these shear stresses cannot be isotropic. Since they are not isotropic they can not be pressure which is only the isotropic part of the stress tensor.

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