Mathematical calculations know as Finite Element Analysis can tell engineers where mechanical stress is occurring
I be one a them that engineers that does stress analysis. (Reading some of these replies goes back and forth between humorous and frustrating. Isn't there a joke about bringing a crayon to an engineering fight?)
There are 3 principles here, so where do we start?
1. If you are just resisting bending stress then you need a bigger section. So if the bending stress is bigger where the blade meets the tang, it is valid to try to make the section bigger there. Then a potential failure would move to the next bigger section. If you change the shape of the section dramatically then you introduce stress concentrations which increase the stresses at those points. (You see them called stress risers too, but I don't think I've heard engineers use this term.) So in terms of blade shapes the fine points of the shape may be more important than the thickness. Crude transitions can become weak points. One example of this is where the tang changes height right behind the ricasso or at the guard, especially with stick tangs.
2. Steels used in knives are relatively brittle. Pick up a normal wire coathanger and start bending it, it just bends all you want and never breaks. You have to mangle it back and forth a lot to cause it to fail. Steels used in knives are a long way from this, rather than bend very far they will just break. There are a lot of different steels and heat treats, some are much better in this regards than others. The ones that are more prone to fracture will be especially sensitive to stress concentrations in the blade shape, even small ones. Bend the blade, a tiny little stress concentration is enough to initiate a fracture, then the fracture travels rapidly through the steel.
3. Impacts on the knife cause all kinds of vibrations and harmonics to travel through the steel usually causing lateral bending and this is what breaks the blade. In dynamics a change in shape or stiffness can cause a concentration of force, and a concentration of force causes a concentration of stress. And if the material is a bit brittle this can be the place that stress will cause a fracture.
So if you want a blade with maximum strength against impacts, the thickness of the material and how the shapes transition are very important, along with a steel that has the highest ductility you can find.