I can certainly say it definitely has to do with pressure; in fact, a lot of engineering mechanics (shear, compressive, tensile, and flexural strength, along with practically every modulus in the book) are measured in terms of pressure. Generally speaking, 1 psi is equal to 6894.76 pascals (newtons per square meter). It depends on what you use.
In this case, if you're crushing something against a hard surface, then you should use compressive strength. If you're bending something, typically flexural yield strength or flexural strength (studies sometimes use either term interchangeably, so watch out for that). Here's a little infographic on how to use each type of strength:
In the case of compressive strength, you'll need the area of the side of the object you're pressing against.