Question

what is the difference between stress and pressure??? what is the difference between stress and pressure??? @Physics

Answer 1

Mathematically, pressure is the trace of the stress tensor.

Physically: stress is the set of 9 possible components of the force that can be exerted on a tiny element of a material:

F_xx F_xy F_xz
F_yx F_yy F_yz
F_zx F_zy F_zz

F_xx is a force that is exerted on the face of the material perpendicular to the x axis (the "x face"), and it pushes in the x direction, i.e. it pushes straight down into the material, compressing it (or, if it points in the opposite direction, expanding it).

F_xy by contrast is the force exerted on the x face but pushing in the y direction, meaning it is trying to shear the material, like a hand pushing a skateboard along, or the friction force your hands exert on each other when you rub them together.

Similar definitiosn apply to the other components.

What you can see is that only the F_xx, F_yy and F_zz components correspond to forces that tend to compress or expand the material. If F_xx is not equal to F_yy or F_zz, then there will be a net force that tends to translate or rotate the material, also. To pull out only the part that tends to purely compress or expand it, we define the average:

p = (F_xx + F_yy + F_zz)/3

This object can be seen to be the pressure (or really minus the pressure), becaus it just acts to compress or expand the material. The rest of the stress components describe linear acceleration of the chunk's center of mass, torque on the chunk, or varying kinds of shear stress.

What that also tells you is that for materials that are not under acceleration or torque, and which have zero resistance to shear, such as ideal liquids (liquids with zero viscosity) or gases, all of the stress components must vanish except for the pressure. That's why we can deal with gases so simply.