Difference between hydrostatic and uniaxial pressure I'm confused with these two terminologies. 
Does 'hydrostatic' means every direction while 'uniaxial' means one direction?
What're they usually used for? 
 A: Yes. When you do stress testing of materials (for example, the Brazilian test of a disk shaped test object) you apply stress along a single axis (using for example an Instron machine). This is a good way to measure elastic properties of materials.
On the other hand if you have a pressurized container (for example the hydraulics in your car brake system), then the same force / stress appears along every direction.
Typically you cannot get uniaxial stress in a liquid; and it is not possible to get uniform hydrostatic pressure in a solid (because the concomitant deformation of the solid will cause a stress gradient).
A: I had the same confusion when I was reading some physics papers and after reading quite a few and checking their experimental setups, this is my hypothesis; I could be wrong, but I don't think I am. Pressure is isotropic, ie equal in all directions. It is by nature hydrostatic. There really is no such thing as uniaxial pressure. When people say uniaxial pressure, they are thinking of uniaxial Tension/Compression as an Engineer would understand it. Usually, you would take the isotropic part of any stress tensor to be the pressure.
It all makes sense if you replace pressure with stress whenever you read these papers. It's what is commonly known as an "abuse of notation".
