FEA Stress Linearization

I think it relates to the von Mises or Tresca yield criterion in which the six components of stress at any element of a complex three dimensional object can be "linearized" in order to determine when failure is imminent at any given point...sort of like comparing a complicated state of stress to a simple tension specimen where tensile stress is T/A, T being tensile force and A being the area of the specimen (say a rod or flat).

You can find more information at these links.

I have tried going through those sites, but those site does not describe what is the purpose of linearizations, does anyone have any idea what that is??