Any physics textbook chapter on stress-strain curves will generally mention that stress is force acting upon an area, and when a shape is three-dimensional, that area is the cross-sectional area. However, every example I have ever seen describing this relationship used a prism of some kind, which has the same cross-sectional area along its entire length.
But then I considered a sphere under compression. At first, I assumed the cross-sectional area upon which the force is acting upon would be the equatorial cross-section, but when I went to double-check that assumption, I couldn't find any information on the topic. Perhaps it is the area of contact which would be more accurate? If that is the case, then would differently sized spheres (made of an extremely stiff material) be very similar in terms of resistance to permanent deformation via compression?
To phrase it in terms of a math question: You have a perfect sphere which is 5cm in diameter, made from a stiff material, which is placed between two flat surfaces. When 200 g of compression force is applied to the sphere, it undergoes catastrophic failure. If you have a sphere of the exact same material in the exact same situation, only it is 50cm in diameter, at what amount of force would it likewise break?